I can't think of any software that the end-user pays API fees or even supplies their own API key/token. I've only ever needed to supply that when interacting with APIs directly in a developer setting. That, or open-source projects that require API access from some 3rd party.
I recall a fairly brief period a few years back where Twitter rate limited 3rd party API keys so heavily the apps basically stopped working... so some apps just put a feature in to input your own API key which you could get for free as a developer key at the time.
Passing it on to the users wouldn't have required billing by API key, just gate at authentication instead.
Rate-limit unauthenticated requests per API key and authenticated requests per account. Problem solved. Turn $0.12/month users into $5.99/month users, and don't worry that the 3rd-party apps aren't showing ads - because Premium users don't get ads anyway.