Traditional hash like MD5 and SHA256 are not locality-sensitive. Can’t be used to detect match with certain degree. Otherwise, yes you are correct. Perceptual hashes can create false positive. Very unlikely, but yes it is possible. This is not a problem with perfect solution. Extraordinary edge cases must be resolved on a case by case basis.
And yes, simplest solution must be implemented first always. Tracking post reputation, captcha before post, wait for account to mature before can post, etc. The problem is that right now the only defense we have access to are mods. Mods are people, usually with eyeballs. Eyeballs which will be poisoned by CSAM so we can post memes and funnies without issues. This is not fair to them. We must do all we can, and if all we can includes perceptual hashing, we have moral obligation to do so.