There's no reason you can't have an attestation entity that's based on volunteer hours, provided you can convince sites-in-general that your proof-units are good.
The core theme isn't about cash, but that:that:
1. There are kinds of activity someone can do which demonstrates some kind of distinct actual expenditure of time or effort (not self-dealing.)
2. A trusted agent could attest to that activity.
3. Requiring (proof of) activity gives you an decent way to ward off the majority of bots/spam in a relatively simple way that doesn't become a complex privacy nightmare.
It's a similar outcome to sending CPU-bound challenges to a client, except without the deliberate-waste and without a strong bias towards people who can afford their own fast computer.