Actually, it's true that nothing in crypto community is free, even airdrop as said as free is faulty, back then in 2017 when only submitting ETH address without tasks gives you free token. Ethereum blue was the free coin someone got that time.
There are services that offer an api for bypassing captcha, this can be used by regular users to remove captchas, or by automated programms like scrapers and bots. Such services work by employing actual humans to solve captchas for a payment and sending the results back to customers all in real time. But to work this service needs to have a large pool of workers so that captchas can be finished within their time limit.
It may be possible that Bitcoin faucets actually act as such services, provided they have hundreds of users solving captchas at any given time.