I'd prefer a UX where if I start typing, the chatbot immediately stops talking, with a play button which I can use to let it finish predicting whatever it was on about.

It's a small tweak, but it would be a significant improvement. Especially when I'm trying to type multi-line input and forget to hit Shift-Enter: there's this immediate context switch to get to the mouse and hit a small button, when what I want to do is just keep typing. Normally that would mean the bot wouldn't even start replying before the pause signal gets sent to it.

That opens up an option. You could design a text program that gives both parties the ability to impose a cooldown timer on the other's box. I wonder when an AI would forcibly lock your own box to deliver a message.

Maybe this would be useful if it predicts you're about to say something incriminating.

This is how @Meta AI works as well. the conversation can continue as it generates it's response, you can see the chat bubble visible growing. No need to press stop.