E2EWidgetsFlutterBinding is for now inherits mock text chanllel and http bindings from TestWidgetsFlutterBinding.

https://github.com/flutter/flutter/blob/master/packages/flutter_test/lib/src/binding.dart#L262

This issue is not blocking to web integration tests since test authors can use these 2 lines to clear the mocks:
SystemChannels.textInput.setMockMethodCallHandler(null);
HttpOverrides.global = MyHttpOverrides();

On the other hand these changes are good to have before we enable e2e to a wider range of tests.