Why not ask it to directly mine some bitcoin, or do some protein folding? Let's make proof-of-work challenges proof-of-useful-work challenges. The server could even directly serve status 402 with the challenge.
More importantly do you want to now compete with those that do not bottleneck and lose your traffic ?
This is the paradox, the length you go to protect your content only increases costs for everybody else who isn't an AI crawler.