You could disable CAPTCHAs for Tor at any point, but don't, presumably because there actually is a lot of scraping and other abuse coming through there. I don't think replacing reCAPTCHA is going to make Tor users magically happy. They will just complain about whatever alternative is used.
One thing you could look in to (email me if you'd like more info on this) is the notion of using Bitcoin-based "anonymous passports". The idea here is that someone sacrifices some Bitcoins to miner fees in such a way that they effectively mint themselves a certificate over a public key, without paying a certificate authority. Seen one way, the block chain itself is the CA.
Once such a certificate/"anonymous passport" has been created the owner can sign challenges with it to prove ownership, and if the user is observed engaging in abusive activity it can be blacklisted - forcing another sacrifice of money if they want to keep going.
The downside of this is that of course it relies on Bitcoin. However, there's a whole army of people working on the problem of obtaining bitcoins. There are local traders. There are Bitcoin ATM's being deployed throughout the world. If you want a private way to demonstrate some sacrifice of effort or wealth I don't think there's a better alternative.
Currently there's no convenient GUI for making these certificates. If a major provider like CloudFlare were willing to get behind the concept, such a GUI could be easily built though. For instance I could add it to Lighthouse, which is a cross platform Bitcoin wallet app that specialises in smart contracts.