Those donations can often be arranged to be tax deductible, so instead of letting $Government spend the money you get to direct its course a little more precisely. At larger income levels they often manage to make a donation pay off as "taxes", but also obligate others of their strata socially, and wield control over the recipients ("we'll sponsor your publication for a year of you dont talk about $controversy").

> why the ultra rich, once they've cashed out, create foundations that hand out grants?

Not qualified to say whether this is exactly the case here, but I think this video about charities/funds as power-wielding vehicles bears some relevance: https://m.youtube.com/watch?v=0Cu6EbELZ6I

Disclaimer: not a big fan of the delivery style in the video.

You've hit on a few reasons. Basically: taxes, no more need for money, desire to give back, desire to have a lasting legacy, societal pressure...

And no, there really is very little work done evaluating private foundations. They operate with very few guardrails and oversight is extremely minimal. It is difficult to evaluate the effectiveness of charities, so how do you evaluate foundations that give grants to charities?

I am an academic that studies foundations and would be happy to talk more about it if you have other questions.

They've been through the struggle themselves, and especially in the tech sector, they must've been very interested in their specific field to devote their life to building a large business around it.

Thus when they find themselves with the time and money to support new innovators, they end up handing out grants as that's an easy way to support fundamental research of the sort that they too once did.