However......everywhere else (the nut on all stringed instruments, and the bridge on a solid body), you want to transfer very little (ideally, none) of the strings' energy into the neck or body. Sustain (we obviously want a fair amount of that, or we wouldn't ever buy solid bodied instruments) comes from NOT transferring vibration into the instrument's body and neck - the nut, fret or bridge should present a solid platform that does not move (or does very little movement) so the energy stays in the string.
Yeah, I need to clarify that (so to speak). When you use a well-seated metal nut, it's making the contact between the string and the wood frame more rigid, less squishy. That reduces the energy drawn out of the string, leaving the sound and sustain as they were.
Up in the high frequency range. The highs are clearer because the string isn't able to transfer vibration
in that frequency range through the rigid nut. A softer, more squishy nut will make the high end softer, less clear, shorter sustain.
But meanwhile, the mid and low frequency vibration is still being transferred to the wood frame, through the nut (and the other anchor points). If the frame is soft and flexible enough, it will flex and vibrate, at those lower range frequencies. This is what fights back against the string, drawing down its energy and modifying the sound on the string. It adds background harmonics and a shaped attack profile. Character to the sound on the string.
If you build the entire frame really rigid, then you will transfer very little of the string's energy into the frame. And the sound on the steel string sounds like...a steel string. Bright, metallic, piercing, long sustain. Maybe that's what you want? But we Luthiers mess around with softening the wood frame specifically to modify that sound, to make it sound less like a steel string. To add character that can't be added by pickups and electronic circuits.
But we do different things to modify different parts of the frequency range. Nuts, bridges and tailpieces are made rigid to improve high end clarity. Bodies are made soft and flexible to increase mid-range background harmonics and coloration. Necks are made rigid along their back spine, but compressible along the front. Neck/body joints are made more rigid.
There are lots of structural things we do to play around with the sound of an electric bass. And they are all going on at the same time. They do different things.