Do hash functions for digital signatures need to be preimage resistant?
A hash function which isn't preimage resistent is also not collision resistance.
If I hash a large random message and apply the preimage algorithm I'm extremely unlikely to get the same message I started with, thus finding a collision.
Collision resistance is critical for a hash used in a signature. As you can create forged signatures. Even though you need a bit more in order to forge meaningful messages, such as exploiting internal state collision to make extensions collide and utilize formats like pdf or postscript.