You said some really good stuff about black people in the 50s (and other times, c.f., Whoopie Goldberg) wishing they had differently colored skin.
The idea of black beauty misses the point, in that it is the epitome of racism to say anything other of a country or of a people than that their food is delicious and their women are beautiful.
So you can say that black skin is more practical—it probably is—but it comes with a lot of baggage, and the baggage is the point, not the other stuff, and it cannot be wished away or neglected.
Penis envy is probably the same. Women don't hate being women, I think, so much as they hate the social baggage and abuse that comes with it. There are possibly lots of advantages (as I see it) to being a woman. Being able to make children as a bodily function is a pretty cool trivial superpower, and it brings with it the fact that men will do literally anything to be with you, that you don't have to go into the meat grinder to be killed like vermin when war and other such happens, that women seem capable of enjoying sex more, etc.
But none of that matters if there is all that other baggage and/or you are not allowed to enjoy it by a society that pegs you because of this one stupid property, gender, race, ethnicity, etc., and takes all the good stuff away from you because of it.
That, I think, is the point, the one that is missed. Yes, black people are beautiful. Yes, woman are wonderful. Yes, mentally ill people are intelligent/valuable human beings. Obviously. But it still comes with a lot of baggage. The baggage is the problem. The baggage is the point.
The one ethnicity that a great number of Americans (and German hobbyist but that's another story) want to claim is Native American ancestry. As you know there is an abundance of "wannabes" and "pretendians" etc. The reason why this is offensive to Natives -- the fetishization of Natives, wanting to 'be in their skin'--is because they are coveting only one aspect of being Native while dismissing, undervaluing, minimizing the rest of the package: poverty, social problems, discrimination, the whole mess/baggage that goes along with being Native.
They just want the cool part. Or the part they think is cool. But nobody, nobody would want to be the victim of the heinous aspects of racism and discrimination, trust me. And when they "forget" or are woefully or willfully ignorant to such aspects, the whole package, then they're very offensive.
Plus there is the whole power structure, the racial/social heirarchy implicit within society. Whiteys at the top, so to look down from their lofty place up above, to disregard their ease and passport within society which is soley structured for the advancement and comfort to fit their needs-- this is also highly offensive.
One aspect I've kind of heard bits and pieces about -- it kind of comes up in racial/ethnic liberation discussions -- is that oppressed groups tend to be mutually supportive, much more so than whitey would be. I could cite examples and anecdotes. It could also tie into the appeal of fanaticism (which otherwise seems pretty unappealing for members, obviously), which is another theory I'm working on.
Whitey may envy this idea that minorities do favors for, are kinder to, and more intimate with other members of their group, which is not a property that whitey (or other majority groups?) share. It's lonely being whitey, apparently much lonelier than the folks that whitey rides herd over. There's not a lot of intimacy and support among white people, e.g., "white trash" etc., i.e., willingness to reject "one's own kind." I'm not sure if I can think up specific examples of whitey expressing explicit envy for minorities for this specific reason, but it may be sublimated in fairly obvious ways.
The Japanese and Chinese may be fairly intolerant of members of their number that "let the side down" but I'm not sure how they measure up in the "mutual support" department, i.e., if the "self-alienation" is a uniquely whitey thing.
NWA (I think) put out "Fear of a Black Planet" back in the 80s, and that is a fear, but a more likely one for whitey may be "Fear of a Chinese/Japanese Planet". Europe (and America) has always been afraid of the Far East, fearing that they may, in fact, be "superior" or have a "more advanced culture". The fear of being a servant in your own country to East Asian masters, and having to figure out how to cook rice in a high-tech rice cooker covered with buttons marked in Chinese characters, I think, haunts the back reaches of the Western (American) psyche.
So, I think you're absolutely right. If a white person can ignore the centuries of brutal oppression and the effect on one's individual psyche and overall cultural identity, in other words, take a completely superficial and shallow view, then being a POC might seem rather better than being a whitey, since whities are perhaps rather a lot lonelier and isolated than POCs, probably a lot more afraid (in their own way), and generally pretty boring for lots of other reasons. In the interest of keeping a "united front" vis `a vis minorities, and since there are just more of them, I think individual whities are seen as "expendable" with respect to the rest of the group, which may not be the case with minorities, where everybody matters and solidarity may be more the rule. This is kind of along the lines of Tim Wise's take on the negative effects of racism on the oppressor race, for instance.
This brings up another point which is how much worse the actual oppression of non-whities must be from whitey's own perspective, i.e., without an understanding of the coping mechanisms, e.g., the mutual support and self-identification that oppressed peoples seem to have, and what does that say about whitey's attitude and perspective towards their role in the oppression?