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>> If CAPTCHAs are intended to be "completely automated public Turing test

That's what google says the are for, but they aren't used that way by everyone. Many websites use them not to detect machines but to slow down the humans. They want to make something burdensome so they add the captcha. Maybe they want you to subscribe, pay money, to avoid it. Maybe they just want you to spend a few more seconds looking at of some banner ad. Or maybe including a captcha ticks a useless security box on some compliance form.

> If CAPTCHAs are intended to be "completely automated public Turing test to tell computers and humans apart", then its quite clear that they no longer accomplish this. I am a human and I can't pass. The model is wrong, build a better one.

Google’s CAPTCHA probably knows that you are a human, some of your answers are correct, and Google already uses the answers you give to improve its Maps offering like it always has. The fact that it still won’t let you pass is presumably a way of punishing you for trying to stay anonymous.

There are not. They are here to save money.