The why did anyone ever wear it? By your logic, wouldn't everyone just go into battle naked and thus have the greatest amount of mobility?

Fine functional (iron) plate armor restricts mobility less than you think. And when you can construct it form 1/16th or 1/32nd thich plates instead it gets even better. When we change the discussion to a scale mail variant then the discussion of mobility becomes even less relevant. A C scale jerkin would probably weigh less, and restrict less than a leather one, and warders have been shown to wear that regularly.

No matter how you slice it (no pun intended) C, as a material for armor, makes excellent sense.

As for your suggestion for plated city walls or gates, there would indeed be benefits, though far less often. Absent rams and trebuchets, city walls and gates are resiliant even when made of stone and regular iron because there is no real need to be concerned about weight and mobility.

It is those 2 concerns that makeS C be so effective. Use of armor has always been a trade off between better protection, and the weight a being or vehicle can handle with the mobility limitation that weight causes.

Iron is approximately 480 pounds per cubic foot. 40 pounds of iron is about 144 cubic inches. 144c ubic inches flatened to about 1/16th inch creates a sheet of iron about 3' by 10'; yes that is right feet, not inches. If you can actually manage to roll the sheet to 1/32nd you doubble the size of that final sheet. Even when you factor in that C is heavier than a like mass of iron (we don't know how heavier, just that it is mentioned several times as fact). a full suit of C plate armor would still only be about 20 to 40 pounds (depending on how thin your technology/skill allows you to roll the iron).

When you consider that the swords warders swing around weigh the better part of 10 pounds, the weight of armor (because it is distributed around the body) would hardly be noticed.