There are certainly some blacks who value lighter skin and straighter hair, but saying that they really want to become white makes as much sense as saying that a white woman who gets a tan really wants to become black. Two other major problems:

plenty of black people would take it, what would increase status gap even further, until only tiny fraction of people stayed black.

This does not follow. It would depend on what subgroup took it and which did not. I also think you seriously need to go talk to some actual black people before you make this claim.

There's earnings gap, lifespan gap, larger chance of being a crime victim when you're "Black". It's naive to think that people would stay "Black" voluntarily if it was a matter of choice.

You assume that, holding all else constant, but changing people's skin color, all these things would go away. This actually sounds like cartoonish, 18th-century-style racism to me. I would love to see some theoretical description of the problems faced by blacks such that merely changing their skin color/facial features would solve most or all of these problems - I rather believe they're caused by complex social, cultural, and economic factors that are ultimately independent of race. You could carve out a subsection of whites with similar characteristics, if you picked the right selection criteria.