Some do, some don’t. Bill and Warren are of course prominent examples of billionaire philanthropists.
Conversely I could name on famous multimillionaire frequently in the news these days, that has a track record of treating charitable foundations as tax dodging piggy banks. So there are all sorts.
I agree they probably stop caring about their tax bill because they are billionaires. I find it disingenuous however to then look down the income ladder to people earning more than $1 million and including them in your “we don’t pay enough taxes” bucket.
It's not the same, but even if you are not a billionaire, there comes a point where giving relatively more of your added income serves a greater good (i.e. funding for gov't) than the money just being in your bank account. Once you make more than you need to keep up your lifestyle (at whatever level that may be) the suggestion to give back more is not unjustified.
There are a lot of very wealthy philanthropists, and I think that's because people seek meaning in their life once they no longer get benefit from earning more.