> This means that it's pointless for them to show their custom prompt if you've already refused access, because even if you agree, they can't get the system prompt to show up again. So you can probably make the repeated prompts disappear

No. I have seen this defeated on a few apps-- they harass you with the custom messages, and when it realizes it can't trigger the system prompt, it just tells you to go into settings and approve it manually. Failure to follow through means the custom messages will continue harassing you as long as the permission has not been granted.