The thing is: We have a binary definition of safety for cryptographic hash functions, and it works well.
You can add a non-binary sense of safety to cryptographic hash functions, but it makes stuff a lot more complicated for no good reason. If you use the "preimage-safe-but-not-collission-safe" ones, you need to do a lot more analysis to show safety of your whole construction. You could do that, but it gives you no advantage.
