It is possible to donate appreciated stocks. And the tax rate can be higher than 37%, if it's short-term gains in California since there's state tax as well.

To run the numbers on the 37%:

Charity: 5.7B deduction * 0.37 rate = 2.109B value of the tax deduction

Selling: 5.7B deduction * (1-0.37) = 3.5B value of the stock sale

In addition, the shares were at an inflated value - if he dumps 5.7B onto the market, it's going to drop the value of the remaining 100B of shares. Whereas by donating to the charity, you get the 5.7B deduction, and the fund you donated to does not even have to sell the stock. Even if the stock drops shortly after, such as in this case, he still gets to keep the large deduction. See https://dlj.law.duke.edu/article/insider-giving-avci-vol71-i..., illegal but unenforced.

Also, he can use the charity money anyway to pay for various things he feels like spending money on - other billionaires have used personal charities to settle lawsuits, employ their children / cousins, invest in businesses of friends, etc.