Mine doesn't mind either which is great (not that I've been into the office since March 2020!). I am competing with my son who is aiming to be able to sit on his hair and he's pretty close; mine just goes outwards unless I nail it to my scalp.
That's a really clever and interesting idea - I'd never thought of something like this. I'm not sure I'll change to it (muscle memory!), but it's really neat.