What about SUTs (set up transformers). Should that be a separate category for those with MC cartridges?Not really. Some phono sections have enough gain on their own.
I think you will find that the ability of the tone arm to properly track the cartridge is far more important than the cartridge itself. So the way the two work together is important and no all cartridges work in all arms.
The job of the platter pad is to absorb vibration from the LP as the cartridge is playing it. It has to be able to do this while not imparting any noise (talking back) of its own. At the same time it should be able to apply additional damping to the platter itself. In turntables minimizing resonance and vibration is what its all about!
The phono section can contribute ticks and pops that sound for all the world as if they are on the surface of the LP! This is due to poor high frequency overload margin and stability issues; and IMO/IME is an epidemic in phono section design.