It'd be a bit of a pain, but it's not restrictive, and most already do that on faucets, so doing another one to send the bounty report won't really matter to them. Bot owners could of course pay for the services that solve captchas for their bots, but it could reduce the number of bots (or so I want to believe).
The "only" downside I'd see is that depending on the captcha type, it wouldn't be very TOR friendly
Well I have suggested that before but there's already a captcha and the bots are getting past that and I think they can get past the other more complex ones so it's a case of how annoying it is to genuine users vs how many bots it potentially stops. Captchas can be very annoying to new users, especially when they take repeated efforts to pass like they do with tor whereas a bot doesn't care and it will keep trying until it gets past it somehow or like you said they'll pay people to solve them which can be done very cheaply. Maybe we could require a captcha if the new user makes a post that contains an url or the first handful of posts a new user makes containing an url need to be approved by a mod before they go live (they could still appear as posted to the user essentially being shadowbanned until verified).