the argument for wrapping your hands is so you can engage in prolonged striking in training without damaging your hands.
The Idea behind engaging in prolonged striking in training is to be good at striking.
Your logic here is A = B, B = C, therefore A = C. Where:
A = wrapping hands
B = safely train prolonged striking
C = being good at striking
(or at least contributes to it)
Therefore: Wrapping hands leads to effective striking
Because there is repeated stress on the hands in boxing training on the heavy bag and in actual fighting, this logic applies. But what does hitting the heavy bag do? There are several advantages, but the most relevant for this discussion is that, firstly, it builds power. In particular, driving. crushing follow-thru power. (One doesn't stop as soon as the hand makes contact with the bag's surface.)
Why is this kind of power necessary in boxing? Since padded gloves are worn there is a lot of shock absorption before the punch force really takes effect. "Heavy hands" are needed to cause real damage (unless one aims to simply cut up the opponent for a TKO strategy). Secondly, extended work on the heavy bag builds muscle and cardio endurance. It's quite the workout.
So, I think
I've defended your position in regard to boxing and your logic. But what is not taken into account is that there are other methodologies that are NOT dependent on A and B that contribute to effective striking, C.
Okinawan karate uses such a methodology. The kind of force required is different than described above. As karate is a bare-knuckle combat art, there is no power absorption by gloves. Hard knuckles make direct contact upon the opponent. This means damage is done with much less drive and follow-thru required.
Our punches (and kicks) are more of the snapping kind, fast and loose, adding power at the point of impact with very little follow thru. I assure you they are effective having been on both ends. And since self-defense encounters typically last less time than a boxing round or two, endurance is less of a concern. Not to mention that in karate the hands don't do all the work, much of the load taken up by elbows, locks and kicks.
So, karate is less reliant on the benefits of prolonged heavy bag punching work. Some of that time is spent training alternative methods of effective striking. Less heavy bag work and less hand/wrist stress in training, and less hand to body contact in actual application over extended time = less need for wraps.
All of this leads to different arts can be effective by using different methods. The sprinter and 10K runner are both good at running, but their running is different as is the way they train. I'm sure there is some overlap, and I think karate training should include some heavy bag work for its full range of benefits. We should be open minded and not think one way is the only way.