There's a layer 2 technology called Lightning Network that lets you transfer Bitcoin almost for free and in seconds, no transaction number limit. The biggest issue is liquidity, it's not easy to move large sums in a single transaction, but that shouldn't matter much for micro-payments.
There's even ongoing work on making paid API's work seamlessly by adding some middleware, using the HTTP 402 (payment required) status code, no usernames/e-mails/passwords involved: https://lightning.engineering/posts/2020-03-30-lsat/
(And yes, LN is open source, non-custodial and moves real Bitcoin, not IOU's or other tokens. It's actually an open spec with at least 3 major implementations in 3 different languages.)
Even if you had to pay 1 satoshi for 10 queries, it would go a long way towards making APIs viable long-term.