Yes, fraud proofs work similar to that: you need to publicly prove that you requested a transaction but didn't get the intended response. If these requests (or the mint's commitment to process a valid request) could be audited by anyone, it should be possible to prove a mint is denying it's service or acting maliciously.
Discussion
Fraud proofs are hard because you can’t easily prove that you aren’t hiding shit from the mint. Broadcast it on a relay the mint can’t read from (IP blacklist for example), and you just framed them for something they couldn’t respond to.
That's why it's best to combine it with a challenge-response scheme: To prove that the mint has replied correctly to a request, it just replies correctly to it.