The key is in “variety”. I was born with the “big” tripos - minority, female, WC. My life experience will be “typical” in some respects but not in others. My DC grew up in relative affluence, their economic life experience is very different from mine but common in some aspects of race (not all because you can’t entirely separate race, class and sex).
What really matters is the mix. Recruiting to ensure you have a wide variety of backgrounds and categories in the mix does make for better performing teams overall in most industries. A board which defines diversity as photos of different races where all members are still male,, public school and Oxbridge will not be much more diverse than the same board where all the faces are white.
At an individual level no one person is the spokesperson for all of their $CATEGORY and shouldn’t be but if you have enough overall variation and not just a couple of representatives for ticking boxes you end up with better and more imaginative teams.