diff --git a/packages/babel-core/src/parser/util/missing-plugin-helper.js b/packages/babel-core/src/parser/util/missing-plugin-helper.js
index 89f6dc91c9..5a5f7082f2 100644
--- a/packages/babel-core/src/parser/util/missing-plugin-helper.js
+++ b/packages/babel-core/src/parser/util/missing-plugin-helper.js
@@ -129,16 +129,6 @@ const pluginNameMap = {
       url: "https://git.io/JfeDR",
     },
   },
-  logicalAssignment: {
-    syntax: {
-      name: "@babel/plugin-syntax-logical-assignment-operators",
-      url: "https://git.io/vAlBp",
-    },
-    transform: {
-      name: "@babel/plugin-proposal-logical-assignment-operators",
-      url: "https://git.io/vAlRe",
-    },
-  },
   moduleAttributes: {
     syntax: {
       name: "@babel/plugin-syntax-module-attributes",
@@ -226,6 +216,16 @@ const pluginNameMap = {
       url: "https://git.io/vb4yp",
     },
   },
+  logicalAssignment: {
+    syntax: {
+      name: "@babel/plugin-syntax-logical-assignment-operators",
+      url: "https://git.io/vAlBp",
+    },
+    transform: {
+      name: "@babel/plugin-proposal-logical-assignment-operators",
+      url: "https://git.io/vAlRe",
+    },
+  },
   nullishCoalescingOperator: {
     syntax: {
       name: "@babel/plugin-syntax-nullish-coalescing-operator",
diff --git a/packages/babel-core/test/api.js b/packages/babel-core/test/api.js
index 8fb5fc1903..384ed74218 100644
--- a/packages/babel-core/test/api.js
+++ b/packages/babel-core/test/api.js
@@ -804,10 +804,10 @@ describe("api", function () {
         options,
         function (err) {
           expect(err.message).toMatch(
-            "Support for the experimental syntax 'logicalAssignment' isn't currently enabled (1:3):",
+            "Support for the experimental syntax 'doExpressions' isn't currently enabled (1:2):",
           );
           expect(err.message).toMatch(
-            "Add @babel/plugin-proposal-logical-assignment-operators (https://git.io/vAlRe) to the " +
+            "Add @babel/plugin-proposal-do-expressions (https://git.io/vb4S3) to the " +
               "'plugins' section of your Babel config to enable transformation.",
           );
           done();
diff --git a/packages/babel-core/test/fixtures/api/parsing-errors/syntax-and-transform/file.js b/packages/babel-core/test/fixtures/api/parsing-errors/syntax-and-transform/file.js
index 0cb4253cd4..9fbdc7e744 100644
--- a/packages/babel-core/test/fixtures/api/parsing-errors/syntax-and-transform/file.js
+++ b/packages/babel-core/test/fixtures/api/parsing-errors/syntax-and-transform/file.js
@@ -1 +1,3 @@
-a ||= 2;
+(do {
+  x;
+});
diff --git a/packages/babel-parser/src/parser/expression.js b/packages/babel-parser/src/parser/expression.js
index 1a7c973e09..6bcb866035 100644
--- a/packages/babel-parser/src/parser/expression.js
+++ b/packages/babel-parser/src/parser/expression.js
@@ -229,12 +229,6 @@ export default class ExpressionParser extends LValParser {
       const operator = this.state.value;
       node.operator = operator;
 
-      if (operator === "??=") {
-        this.expectPlugin("logicalAssignment");
-      }
-      if (operator === "||=" || operator === "&&=") {
-        this.expectPlugin("logicalAssignment");
-      }
       if (this.match(tt.eq)) {
         node.left = this.toAssignable(left);
         refExpressionErrors.doubleProto = -1; // reset because double __proto__ is valid in assignment expression
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals-no-plugin/input.js b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/and-and-equals/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals-no-plugin/input.js
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/and-and-equals/input.js
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/output.json b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/and-and-equals/output.json
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/output.json
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/and-and-equals/output.json
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/input.js b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/mallet/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/input.js
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/mallet/input.js
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/output.json b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/mallet/output.json
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/output.json
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/mallet/output.json
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals-no-plugin/input.js b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/qq-equals/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals-no-plugin/input.js
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/qq-equals/input.js
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/output.json b/packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/qq-equals/output.json
similarity index 100%
rename from packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/output.json
rename to packages/babel-parser/test/fixtures/es2021/logical-assignment-operator/qq-equals/output.json
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals-no-plugin/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals-no-plugin/options.json
deleted file mode 100644
index 5b674fdee4..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals-no-plugin/options.json
+++ /dev/null
@@ -1,4 +0,0 @@
-{
-  "plugins": [],
-  "throws": "This experimental syntax requires enabling the parser plugin: 'logicalAssignment' (1:2)"
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/input.js b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/input.js
deleted file mode 100644
index 740f1fa926..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/input.js
+++ /dev/null
@@ -1,2 +0,0 @@
-a &&= b;
-obj.a &&= b;
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/options.json
deleted file mode 100644
index 5041dbb19f..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/and-and-equals/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": ["logicalAssignment"]
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/input.js b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/input.js
deleted file mode 100644
index 53c87792bb..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/input.js
+++ /dev/null
@@ -1 +0,0 @@
-a ||= b;
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/options.json
deleted file mode 100644
index 5b674fdee4..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet-no-plugin/options.json
+++ /dev/null
@@ -1,4 +0,0 @@
-{
-  "plugins": [],
-  "throws": "This experimental syntax requires enabling the parser plugin: 'logicalAssignment' (1:2)"
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/options.json
deleted file mode 100644
index 5041dbb19f..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/mallet/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": ["logicalAssignment"]
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals-no-plugin/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals-no-plugin/options.json
deleted file mode 100644
index 64389a4588..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals-no-plugin/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "throws": "This experimental syntax requires enabling the parser plugin: 'logicalAssignment' (1:2)"
-}
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/input.js b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/input.js
deleted file mode 100644
index dcf876b174..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/input.js
+++ /dev/null
@@ -1,2 +0,0 @@
-a ??= b;
-obj.a ??= b;
diff --git a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/options.json b/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/options.json
deleted file mode 100644
index 5041dbb19f..0000000000
--- a/packages/babel-parser/test/fixtures/experimental/logical-assignment-operator/qq-equals/options.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-  "plugins": ["logicalAssignment"]
-}