If you look at elliptic curves I don't think there has been any big changes in attacks for 20 years but some attacks like MOV or SMART would have been fatal to EC if they had applied to more curves. So maybe there is some unknown attack that applies to all curves or applies to a small subset of curves that happens to overlap the curves we use. If you are super paranoid you should probably use curve25519 because then at least you can be confident it was not deliberately engineered to be weak. it could still be weak by chance but presumably the designers did not have enough flexibility to choose the parameters to make it weak. Some people are paranoid about the NIST curves because there is no verifiable explanation for where the seeds came from. But if the NIST curves were made weak then I think its a situation where theoretically anybody could find the weakness which is very dangerous. I don't think it was possible to create a no-body-but-us backdoor for the NIST curves.

Also, even if DLP is hard for the curves we use algorithms like ECDSA might be a bit fishy. Unlike schnorr signatures there is no proper security reduction for ECDSA.