I see what you are saying. But if you aren't using a cryptographic hash function then collisions don't matter in your use case anyway, otherwise you'd be using a cryptographic hash function.
For example, you'd use a non-cryptographic hash function for a hashmap. While collisions aren't exactly desireable in that use case, they also aren't bad and in fact, the whole process is designed with them in mind. And it doesn't matter at all that the distribution might not be perfect.
So when we are talking about a context where collisions matter, there's no question whether you should use a cryptographic hash or not.