In theory, the ability to understand discrimination issues isn't tied to being a minority, but in practice, if you have a group of non-minority people, no matter how much theoretical knowledge they have, they're extremely likely to miss things pertaining to discrimination which would not be missed by a more diverse group. Diversity in and of itself produces observably better outcomes. There's underlying mechanical reasons for this, and there's actually several different types of "diversity", and all of them at least somewhat matter.
Also be aware that "the best person for the job" is absolutely contextual. I'm a very good programmer. I'm also a bit of a flake in some ways, but also very creative and non-traditional. So for a team that doesn't have someone like me, I'm an incredible candidate -- I will add immense value that they do not currently have. But if you already have a couple of people like me, another one isn't gonna do you much good, and a more "boring" candidate who's just good at getting stuff done is going to be much more valuable. That's more in the realm of psychological diversity rather than ethnic diversity, but it turns out that ethnic and cultural diversity are strong predictors of psychological diversity. If your team is not currently particularly diverse, increasing diversity will bring significant benefits.
Another consideration is that there's a lot of metadata and signalling. Part of the role of a "manager for diversity, equity, and inclusion" is to inspire confidence in other people that these things matter, and that, for instance, it's worth bringing concerns to this person when appropriate, and the workplace will be welcoming for members of minority groups. If you've tried two or three times in the past to bring up concerns about blatant or excessive harassment or discrimination to people whose job title was something like "manager for diversity, equity, and inclusion", and had them blow it off because they didn't really understand or care about the issue, and all of those people were white guys with college degrees who could use the buzzwords but had no skin in the game, you may be reluctant to bring an issue up with another white guy with a college degree and no visible skin in the game. And that means that, in practice, the white guy may not be able to do the job as effectively. Which is hilariously ironic, but also turns out to matter, if you're trying to fix a problem.