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.
Imagine if you were the owner of a really large computer with CSAM in it. And there is in fact no good way to prevent creeps from putting more into it. And when police come to have a look at your CSAM, you are liable for legal bullshit. Now imagine you had dependents. You would also be well past the point of being respectful.
On that note, the captain db0 has raised an issue on the github repository of LemmyNet, requesting essentially the ability to add middleware that checks the nature of uploaded images (issue #3920 if anyone wants to check). Point being, the ball is squarely in their court now.