WebView doesn't bring up keyboard on text fields

I am experiencing this issue on Android devices using the example provided here:
https://github.com/fluttercommunity/flutter_webview_plugin/blob/master/example/lib/main.dart

Tapping on a text field on a webpage within webview does not make a focus node (not sure if that's the right terminology). No keyboard is coming up and tap-and-hold doesn't bring up the copy/paste/etc dialog. A curser is blinking but does not seem focused on the text field.

Tested this on Samsung Galaxy 9+ and the nexus5 / pixel c emulators and ios emulator (ios12.2 iphone 10s).