I don't think this has actually been proven as of yet, since "best" is a very loaded word, especially you're required to measure on more than one axis. (But feel free to point me to any source that disagrees with me.)
It's like if you were tasked with buying the most powerful engine produced for a locomotive. How you define powerful is arbitrary and is an optimization problem on its own, but if you then say "and the engine block must come from the factory painted red" you are, by definition, no longer optimizing for the fastest engine, you're optimizing for the fastest red engine. Being red is independent from being the best engine.
I do not approve of DEI methods as they usually get implemented in capitalist tech companies, but the underlying idea, encourage more groups with lower representation to participate in tech is sound, and it is what I'm advocating for in this exchange.
Western tech world is biased in favour of middle-class white men due to the fact that it's made out of mostly middle-class white men. You might not agree that's a problem, but most of the world does.
DEI is to prevent the kind of favouritism/nepotism that prevails in a lot of society (e.g. "the old boys club"). A suitable example would be the recent hires by the U.S. administration - people are being given high ranking jobs just because they're loyal/friendly to a certain person and nothing at all to do with their competency to do the particular job.
The purpose of DEI is to allow the most qualified person to get the job despite the overt racism and sexism in society.
Humans gonna human.