That sounds disconcerting and distracting; I don't want my prompt to change while I'm typing a command. If I already have a command prompt, I can type "git status" easily enough.
Ah, I see. Interesting zsh magic, and the right-prompt mechanism makes it more palatable. Two issues, though. First, I use bash. Second, and more importantly, you're using the same temporary file for all shells, so the prompts from different shells (in different working directories) will overwrite each other.
Yeah, I thought about using a different temp file per shell, and I did use that for some time, but that got annoying when shells didn't exit gracefully and clean up the temp file.
I don't actually care about race conditions (okay, the wrong prompt may be displayed once, big deal), and it doesn't actually happen in real use because of the way timing works out.