No, that's not what Federal anti-discrimination law says. It only says you can't refuse to hire certain people on the basis of a protected characteristic (of which race is one, but not the only one). It says nothing about refusing to hire certain people for other reasons that don't have to do with a protected characteristic.

(Btw, corporate boards of directors aren't even "hired"; they aren't employees. So it's not even clear what, if any, Federal anti-discrimination laws about hiring and employment would apply to them.)

> Given that these boardrooms don't diversify themselves, what is the actual problem with it?

There are two actual problems. One is that you can't have a government that only exercises its power wisely. For every mandate the government makes that happens to move things in the right direction, there will be many more that move things in the wrong direction. The people who are attracted to government jobs where they get to tell other people what to do aren't benevolent helpers; they're people who like power. All history shows that such people are precisely the people you don't want telling other people what to do.

The second problem is that dictating that people of certain races must belong to corporate boards is just as wrong as dictating that people of certain races can't belong to corporate boards. Both are looking at something that is irrelevant to the actual job, which means they aren't actually improving the corporations; the corporations can still do just as much damage as they did before, just now they'll be doing it with a "diverse" board.

The only real way to fix corporate governance is for people who would do better jobs than the board members of current corporations to form their own corporations and out-compete the current corporations.