It's almost like, if they already know you're not a bot, they don't have to try very hard to re-prove it, or something.

Think of it in a Bayesian sense.

If 10% of anonymous users end up being bots (the prior), and the "hard" recaptcha has a 1% false-negative (incorrectly identifying someone as a human) rate, then of the anonymous users who succeed in getting past the recaptcha, .1% will be bots (the posterior).

But if 1% of sign-in users are bots (probably less than that), you only need a recaptcha with a 10% false-negative rate to achieve the same bot throughput limit. And, those users are less frustrated.