The following design is possible:
1) miner ONE (human) makes a captcha and the client app submits it to a pool server
2) miner TWO (human) gets a random captcha from a pool server and submits back the answer
3) random p2p clients (human) get both the original captcha and the answer and verify that the answer is correct
4) if the answer is correct a block is created and miners ONE and TWO get a reward
5) p2p clients also get a small reward but for just verifying (kinda transaction processing), regardless of whether the answer was correct and their intention is to keep the blockchain healthy as only then their earnings make sense
1) Botpool 1 generates a huge number of captchas and submits them to the pool server
1a) It also passes all of the generated images and solutions to botpool 2
2) Botpool 2 repeatedly requests captchas from the pool server. If the image matches one it already has from botpool 1, it submits the correct answer, otherwise it just burns it and requests the next.
3) Some poor sods have the job of verifying all this bot generated work for almost no reward
Computers could generate and match these images so fast that no human actors could possibly compete.
This can be avoided easily:
1) to submit and answer captchas you need to register and the submission rate is limited
2) coins could vest and if malicious activity is found out then all non-vested coins get confiscated
3) when miner 2 gives a wrong answer the verifiers mark him as untrusted
They are botpools, they have multiple connections, so submission rate limits aren't going to work.
You can't dump anyone who gives a wrong answer, humans frequently fail captcha, and even if you do dump one bot, they can just cycle to a new connection.
The only human element required would be creating new accounts and feeding those details into the botpools.
Even ignoring the answering aspect, the first botpool could create captchas, and feed them in through multiple accounts, far faster than any human could, and just take that part of the payout. The moment your network started, 90%+ of the captchas could be computer generated, in which case the second botpool is almost guaranteed to get a captcha it already knows the answer for.
The system would fail because the human verification step would be orders of magnitude too slow.
To make it work, you would have to make that verification step the key point.
(Although at that point, botpool 3 would step in and do verifications for all those captchas it already knows the answer for)