Handy already supports streaming transcription models, and you can see the words in the small Handy pop-up while you are talking.

So in general this definitely works. Handy is just missing the feature to insert these streamed words into the app where the cursor is.

I suspect the hard bit is that it sometimes needs to back up and redo, and that's an interface they haven't got figured out. I'm fairly sure I remember Dragon Naturally Speaking doing it in Word years ago though, so the interfaces should be there.