@chipsnblip I've also tried with my iPad charger (5.1 volts at 2100 mA) and the same issue occurs with exactly the same repro steps.
This morning I tried a different distro (batocera-linux -- derived from Recalbox). Everything works without any issues on my PiZero W (NES, SEGA GENESIS, SNES). The only difference in my setup with batocra-linux is that my controller needs to be on the "D" switch instead of the "X" (my controller was not working in "D" mode with RetroPie). Maybe that's another clue to investigate. For the time being, I'll stick with batocera-linux since It Just Works™.
I will still be monitoring this thread as I am curious if anybody else is able to reproduce. I can't be the only one having this issue.