Exactly. Another aspect to it is that taxes eliminate the free-rider problem.
If I, as a socially-minded millionaire, make a lot of philantropic donations, but my neighbor, the not-so-socially-minded millionaire doesn't do that and instead uses their money to fund a think tank that lobbies for the abolition of social welfare, then we have a problem.
Rather than engaging in philantropy, it is more rational for me to fund a think tank that lobbies for the expansion of the social welfare system.
If your millionaire neighbor is genuinely less "socially-minded" than you are, it's not clear whether she would actually be "free riding" on your philanthropy. "Free riding" generally means getting a benefit that you strategically avoid paying for, not just having different preferences.
Now, there might nonetheless be a case for taxing your neighbor millionaire a bit more, but it would have to be somewhat different. (For instance, you might think that having more millionaires around creates negative externalities in the form of way too much corruption, rent-seeking etc. from aspiring millionaires. This would indeed be the kind of thing that taxes could correct.)
If I, as a socially-minded millionaire, make a lot of philantropic donations, but my neighbor, the not-so-socially-minded millionaire doesn't do that and instead uses their money to fund a think tank that lobbies for the abolition of social welfare, then we have a problem.
Rather than engaging in philantropy, it is more rational for me to fund a think tank that lobbies for the expansion of the social welfare system.