I could also go "as a" = "chrust me", but since this is the same as mincing words to say "yall buncha gullible cows!", I won't. Still, due to the merits of the topic (captcha and potential replacements) I'll still go on.

To be blunt you're in the worst demographic to talk about this from personal experience, as having both at the same time impairs your ability to tell their effects apart. Unless you were specific on "people who have both" (you weren't).

When someone has depression without the social anxiety, the problem is not if something is personal or not. People are... whatever, yet another bloody thing getting in the way of what you want. Just like waking up, shaving, or working on that huge pile of work so you can eat in the next month. (In fancy terms your "sense of agency" goes down the bloody drain.)

Captcha does affect it. It isn't just "irritating". It's yet another bloody barrier. And, as I said in another comment, it will likely get worse over time due to botting improvements. (And likely more egregious too, as people tend to overuse systems falling apart.)

Would this sort of system be another barrier? Yes, I'm not pretending that it wouldn't. Feel free to drop ideas for any system that keeps botters out, without being at least a minor barrier for humans*, given that captcha is likely going the way of the dodo.

Another thing that you ain't taking into account is that some people are really, really eager to offer shit, as long as they have the ability to do so. "I can guarantee people! Do you want to be guaranteed? Please please it's cool!" That's bound lower the barrier of the bother of asking those things called "other human beings" for help, and it makes you feel less like "I'm being helped, do I really deserve it?" and more like "okay whatever I'm playing along to get rid of you".

The issue with the group network version is that a few large corporations would end up taking it over. Again.

Explain two things here.

1. How exactly are you jumping to this conclusion? "Group-based" → "a few large corps will take it over" is not so obvious. This sort of system simply doesn't make sense with only a handful of actors (be them groups or individuals), only when there's a lot of them.
2. The relevance of your claim in this matter, given that this idea is supposed to address bots, not to solve the problem of megacorps vulturing the internet. (It is a real problem, but another can of worms.)

*Another poster mentioned proof of work; it's an idea worth thinking about, although it has a few cons.