Can't change System Security Settings in new MacBook Pro M1 Monterey Startup Recovery Utility
For anyone that has this problem in the future, I seem to have solved the problem. The confusing part is that it actually solved itself. I think it has to do with the disk encryption status - while the disk is initially encrypting changing this security setting does not appear to be possible. After coming back to this setting about 6 hours later, it suddenly started working, for no apparent reason.
I tried completely disabling disk encryption and re-enabling it - and at first, it did not work. But after a few hours, the problem suddenly disappeared. So it appears that changing this setting when you first start setting up your Mac is the problem.