tax write-offs aren’t free money afaik—you still end up with less money than you started with, had you not started the charity.

Exactly. Giving to charity basically just offsets the amount of income you're taxed on. To give a really simplified example, say I'm making $100,000 per year and I'm taxed at 25%, so I pay $25,000 in taxes. But if I give $10,000 to charity and write that off on my taxes, I would be taxed as if I made $90,000 in the year, so I'd pay $22,500 in taxes.

Of course it gets really complicated when you own a business as well as your own tax-exempt charitable foundation and you distribute your money by donating to your own foundation...