Neovim is a superset of vim, so this argument applies to both.

No, Neovim is not a superset of Vim. Vim has things that Neovim doesn't have and vice-versa.

Neovim remove set compatible (hardcodes set nocompatible). Vim support the POSIX vi via that option.

Not quite. Vim is vi compatible by default. You have to explicitly opt in for the newer behavior.

In what circumstances would you run `vi` and find yourself upset that you end up in `vim`?

You won’t, but vi is scriptable and part of POSIX.

It’s a basic infrastructure that you don’t want to break.

Apparently the original vi isn't POSIX compliant; nor is vim. https://vimhelp.org/vi_diff.txt.html#posix

I think "if the script worked before, I want it to work later" has much more practical weight. Though, on the other side of practicality, I've heard sed, awk, and perl suggested for manipulating text in bash scripts far more than I've heard of vi recommended for the task.

Yes. If you need to do some text manipulation in a shell script, `sed` or something like that is what I'd reach for first. (I haven't used `awk` or Perl for quite a while.) I'd think even `ed` would be a more straightforward choice than `vi`.