Yes, I do. Sometimes people want (more) synchronous communication despite the asynchronous medium. Among other things that helps guarantee a speedy response. A lot of people use asynchronicity as a way to simply avoid answering in a timely fashion, so framing it like this can make sense if you can't afford that.

In addition, seeing the chat bubbles appear moments after you finish your round is a good sign the other person isn't multitasking and letting their own attention get fractured.

I never found it rude to begin with, just not using the medium to its strengths. But this has me realizing maybe it's a deliberate way to eschew those strengths, for some purpose or another.