I've seen 4E fans praise the system for the fact that it is very easy to re-skin. You can take nearly anything and redescribe it and with no mechanical change it is something very different in terms of concept. And I can see how that would be appealing.
But the price is that the character isn't really married to the mechanics. So while it is 100% true that you can roleplay anything in 4E that you can roleplay in any other system, that effort is like a completely independent part of the experience. The "game" is over here and the "role play" is over there.
This is the only part of the longer post where I think you really overstate the case. It is not that
any mechanic can be easily reskinned into
any concept. Rather, it is that there is "mechanic set A" which has a certain vibe, and because of that, it works pretty well for concept A, and always for A2 and A3. For B2, not so much.
So the "game" and the "roleplay" are not completely independent. They are more independent than in some other games, including 3E. (Though even 3E is more independent in this way than some games. Just inconsistently so. Some 3E things reskinn easily this way; some do not.)
Actually, I'd say the relative difference between D&D 3E and 4E is about the difference between GURPS 3E and Hero System 4th edition. (Not sure about later versions of those games.) GURPS 3E is more specific, but the underlying framework is pretty obvious, and thus easy to reskin, if you want. Whereas, Hero 4th is clearly a mechanic first, which you can then make it something suitable. It's not an exact correspondence, but I'd guess the relative distances are similar.
Also, the appeal for some of us, along similar grounds to your larger post, is not so much the modest increase in "game" and "roleplay" independence (though that is nice, too, when reskinning is handy), but rather that the "game" elements that we have to work with are, for us, a better representation of the "roleplay" we were trying to do with an earlier ruleset. To wit:
From the 3E to 4E wizard, you gain some independence on mechanics, and you definitely lose some flavor. You might like this because of the toning down of the wizard (a problem for some of us), and you might regain some of that flavor in various ways, but I don't think many people would argue that right out of the box, there is some flavor lost, along the grounds you have supplied.
However, from the 3E to 4E wizard, you gain some independence on mechanics, and you swap one kind of flavor (feat customization, mainly) for another kind (being really good at getting in monster faces). Overall, there is a strong case for the flavor at least being neutral. And of course, if you happen to value the "in your face" part more than the 3E-style customization, this is a net win. It's a strict preference though, and has nothing to do with the independence, whatsoever. The independence just means that if you want an in your face monster, you know how to reskin the mechanics to get one.