I've been doing E2E testing using 3rd-party APIs for a decade now, and this has yet to be a significant problem. The majority of my APIs had a dedicated sandbox environment to avoid "rate limiting, bans, and other anti-abuse mechanisms". The remainder were simple enough that the provider didn't care about users exploring on the live API, and were usually read-only as well.
Did I run into the occasional flaky failure, or API stability issues? Sure. But it was very rare and easy to workaround. It never devolved into becoming "untestable" or "full manual QA"
My other teams that relied on mocks suffered from far worse problems - a ton of time being spent on manual-QA, and bugs that leaked into production, because of mock-reality mismatches.