For example, free bitcoin is one of the most famous taps sites that pay members a few of the Satoshi. Everyone says that this site is free, but frankly, this site is not free, because we can get some satellites, we need to bypass the captcha, so I want to say that the site gets profits from this CAPTCHA. [...]
Okay let's say you're right (I am not familiar on how faucets get their revenue lol) but actually everything makes sense for me. That's why I understand if those sites used the term "free" because you can really get free satoshis without putting money out from your own pocket. Few clicks never bothered them anyway hahaha. Besides, "free satoshis" is more effective and convincing slogan compare to "Get satoshi for clicking" etc. — that's how advertising works.