Although i prefer my Jeep to be dirty and let it sit dirty for a while after i'm in ORT mode, i typically (minimally) power wash the undercarriage:
Possible negative affects are:
Rubber boots (CV boots) can dry out faster and rot the boot.
Dirt in the brake pads rotors - squeaking, wearing pads/rotors
Rocks in tires get flung on the road - (i like to let them hit beamers riding my a$$)
If you do have any damage/leaks from off-roading, the dirt/mud may cover it up.
Good point on the paint - mud/dirt should not mess up your paint, but if someone/something brushes up against it with mud/dirt on there, there's more potential for scratches.
I would say it's up to the owner, but i like to wash the underneath, more of an audit than anything - hope that helps -
Good looking Jeep BTW