It can go either way. A top-down company can be interested or disinterested in culture. Some would argue that for a company to affect disinterest is an active and consequential choice. Consider the "bring your whole self to work" touchy-feely open-plan Valley startup vs a trad IBM-style cube farm. The latter is arguably more accommodating of genuine oddballs, for "good fences make good neighbours" kind of reasons.
As regards pivoting, think about it like a joint having freedom of movement on more than one axis. You want to keep flexibility in as many as possible, but also straight-line speed/strength/efficiency. Somewhere there's going to be a trade-off. A genuinely diverse team (I don't mean just "ticking all the DEI boxes", but profound differences in background and life experience) takes longer to find their groove than a bunch from similar social backgrounds, but they'll have insights that a "TV sitcom cast"-looking team never will.
As regards pivoting, think about it like a joint having freedom of movement on more than one axis. You want to keep flexibility in as many as possible, but also straight-line speed/strength/efficiency. Somewhere there's going to be a trade-off. A genuinely diverse team (I don't mean just "ticking all the DEI boxes", but profound differences in background and life experience) takes longer to find their groove than a bunch from similar social backgrounds, but they'll have insights that a "TV sitcom cast"-looking team never will.