@andrewg But... whoever does invent a workable self-cleaning toilet will never need to invent anything else, assuming they don't just give away the design (but it would be great if they did!).
I don't see trying to invent something that EVERYONE wants as a waste of time. Even if you fail, you have figured out all the ways that won't work, and maybe you can write a book and save other from trying all the things you tried. Or maybe someone else will pick up on your nearest to success effort and figure out what you missed.
But anyway I guess I am not seeing why the fact that there are uncleaned toilets should be a problem for #FOSS. That's not a problem unless you choose to make it one by not cleaning the toilets AND refusing to use an "unclean" toilet. Not to be sexist or anything but I think most women would just clean the damn toilet, whereas many men would let it go for years before they'd ever clean it, and just continue to use it. When I was a kid I had a couple occasions to use a toilet at a place where my dad worked (all men working there) and I don't think it had ever been cleaned from the day it was installed!