On at least some small terminals (like the smartphone size I mentioned in my original comment), I can confirm that this is a true loop. When originally reporting the issue, one of the things I tested was repeatedly pressing the Enter key with an empty password field. In that test, the password prompt looped for the 20 or so times I continued to press Enter.

As an end user, the --pinentry-mode=loopback flag does exactly what I'd want to resolve this issue. Just to give it more visibility, is there any chance we could try to detect when the user's terminal is too small, and print a message suggesting they use that flag?

It's worth noting that this issue is particularly impactful for devices with small screens whose sizes cannot be changed. A Raspberry Pi with an Adafruit touchscreen would almost certainly have issues, for example.
This also applies to mobile devices. For context, I use Termux on my Android phone, and this issue manifests there. I can enter the passphrase for an existing key and decrypt/sign with it, but any attempt to create a new key throws me into the same loop that the OP describes. (Interestingly, this happens whether or not I actually supply a new passphrase.)
Since I am on a mobile device in this scenario, my terminal dimensions are 56x115. I'm not familiar with the implementation details of GPG, but is there any chance we could fall back to a single-line, sudo-style password prompt if pinentry fails (or have pinentry fall back to that internally if the normal mode fails)? That should work on terminals of just about any size.
(As an additional note, I've also tried flipping into landscape orientation, hoping that would increase my screen width sufficiently. However, my keyboard then occupies most of the screen, and I receive the expected error message, gpg: agent_genkey failed: Screen or window too small.)
EDIT: I'm running GPG 2.3.1 and pinentry 1.1.1.