I get that some people will consider this beside the point, but underrespresentation of black coaches relative to black players seems to assume that playing ability and coaching ability are strongly linked, and what is the evidence for that? The plot points are all over the place.
The best coaches right now -- BB, Andy Reid, Mike Tomlin, Doug Pederson -- never played in the NFL. Vrabel shows promise and there have been NFL players who were great coaches (Mike Ditka) or at least decent ones (Art Shell). But surely there are many counterexamples -- Mike Munchak was a nine-time Pro Bowler and, though not as decorated, I get the sense Herm Edwards was a really good NFL player. Both bad coaches. I would be curious to see a list of former NFL players turned HCs and how they fared. My guess is not only no better but likely much worse than coaches who never played professionally because they require different skill sets, and a player who never played professionally typically gets a head start on coaching and learning to coach. Just look at the most accomplished black coaches of all-time. Tomlin, Denny Green, Marvin Lewis didn't play in the NFL. Tony Dungy had a very brief career and switched over to coaching pretty early.
Even if the very best NFL players would make the best NFL coaches, perhaps they have all been paid too well during their playing days to want that kind of grind when they retire, so perhaps your best bet for a good HC -- among people who want the job -- is still someone whose entire post-college career has been spent coaching. Brian Flores is another one.
I don't know this because I don't have the data to see if there's any correlation between player and coach success, but if there isn't one, that means two things: (1) black men aren't necessarily underrepresented as HCs, and (2) if you want more more good black HC candidates, you have to find good black HC candidates. You can't just bring on former beloved players who want to get into coaching and happen to be black by putting them in a position coach role with a hard ceiling while secretly believing your best internal HC prospects to be former film room and scout types who've been working with coaches (or were raised by coaches) for 10-20 years and have been developing what you believe to be a HC skill set. Instead, you have to hire more black men right out of college who are interested in coaching so they can benefit from the years of exposure to coaches' meetings that BB, Reid, Flores, Tomlin, McVey, Shanahan, etc., clearly benefited from.
Also, while I know the strong support for some kind of intervention comes from a good place, a policy to incentivize represenation that's as highly-visible as the NFL's draft pick proposal could very well undermine the much more worthy goal of reducing racial disparities in health, wealth, and economic opportunity nationwide. The egalitarian impulse is good but applying it selectively can be counterproductive. Increasing the number of black HCs from 3 to 25 would improve the material conditions of a microscopic share of black people in this country, while possibly even increasing the popularity and profitability of the NFL. The problem with that is NFL owners drive and profit from (and on and on) many of the broader political and economic trends that create and sustain those disparities in the first place. Beyond owners, political groups that generally oppose measures to reduce inequality tend to do so on the grounds that opportunity has been equal. Most of us agree this is not true, opportunity broadly defined is most certainly not equal, but the obstructionism becomes politically effective the more examples obstructionists have of favoritism, and awarding an extra NFL draft pick is a perfect example.