Your points regarding monohulls are correct (except the rig moves forward relative to the keel creating a moment that will bear you away with heel induced trim) but they are secondary effects. You need to also look at the boat from aft to see a moment created between the keel and rig which tends to turn the boat to windward.

Most (dare I say all) rudders have their centre of pressure aft of the pivot axis. If everything else is equal and you move the rudder pivot axis closer to its centre of pressure the force on the tiller reduces (ie. the force you feel on the tiller), but the force on the rudder blade does not change. The pivot point is chosen to maintain a managable helming force for a given weather (or lee) helm that is best for the conditions.

I think we're arguing the same thing but our terminology is different. Because most boats want to round-up into the wind and the force on the tiller is the feedback we as skippers feel for this effect, they can basically both be called weather helm.

There is a slight difference between cats and monos but the principles are the same, the various forces on the boat are separated by distances creating moments. Those forces change with heel, trim, sail settings and daggerboard position.