"it appears to me that Google is patenting it so that they have the patent, not for purely altruistic reasons"

This is not correct. In fact, as far as i know, the code was already open sourced, and the patent would end up released as part of AV1/etc anyway.

"If it was for the public good, the patent would be filed via a non-profit that Google can't control."

It'll be released that way, so who cares who files and pays the fees?

You really don't want non-profits filing patents. Really. This is pretty much the most horrible thing i can think of. It's infinitely easier to keep them from going bad (Example: MPEG-LA) if you can make their corporate bylaws, etc, prevent them from filing patents.