so you encrypt your image, send it to the government, the government runs its CSAM detector on the encrypted image and gets... an encrypted result.

then what? you decrypt the answer and send it back to them? promise that you totally didn't change the answer?

FHE is the wrong tool for the job. you'd want verifiable computation (e.g. ni-ZKP) instead. both are too complex and faaar too computationally expensive for actual use.