Free tier was something we've had previously but it became hard to justify because of our third party integrations and what it costs us. It might be something we try figure out in the future. Thanks for the feedback.
User completes a human-level task (for another API even) somewhere between CAPTCHA and MTurk to earn a few API calls.
Do something with ads near or even on the result to earn a few API calls. (Prototyping dev eyeballs are valuable.)
But honestly nothing wrong with charging money for a service.