[JohnFen]

> I don’t understand why they being used on a site would be correlated with usefulness.

Simply from personal experience. The majority of the time when I hit a captcha or somesuch, it's been for websites of marginal usefulness to me.

It's certainly not some sort of hard and fast rule -- there are plenty of exceptions as you point out. That's why I consider it a weak signal. But if other weak signals make me doubt the site is useful and I hit a captcha, I'll just move on immediately rather then continuing to spend time checking it out.

I think it's mostly that doing a captcha is a cost to me in time and irritation, and if I don't think the website is worth paying that cost, I won't.