So, to sort of summarize:
In 5e, you can never really be as good at fighting unarmed as you can be fighting with a weapon (which makes sense, as a solid metal blade will be sturdier than a foot).
You can still be reasonably good at fighting unarmed, for various reasons (to be able to attack even when disarmed, to put a slap-patch on someone, for a surprise attack, or what-have-you).
The striking callus should have common sense errata applied by the GM as needed, in case a player asks if they stack or something.
I do also think that, with equal skill, you should be able to hit harder with a club than with a fist, unless you're an adept who's invested that way.
So I don't see much of a problem with the way 5e handles it. I do want to know why 6e apparently de-coupled STR from hand-to-hand weapon damage, and I assume it's due to other reasons we haven't been able to hear yet.