As a dude who had to clean bathrooms. You lie. Ive seen soo many nasty toilets from both restrooms whether it be be seat hoverers or from people who didnt make it.
I don't often use them, but some women's rooms are not that much cleaner than men's. Diarrhea in every stall, piss on the seats, or worse blood from periods left behind. We are all human with bodily functions and some of us are gross shit leaving goblins.
The floor is easy to figure as it happens to me. It's gravity, I stand up to wipe and the blood doesn't stop coming, it will continue to drip and I've had it go down my leg or on the ground depending on how I was moving around. I always wipe up tho cause that's just the normal thing to do. As for the wall, I'm assuming it was on their hands after wiping and they touched the wall. Other than that I really couldn't tell ya as I ain't the one doing it loool it's definitely the grossest shit to just leave it there like it isn't their job to clean up after themselves
Are you sure there isn't a little clear piss on the seat? Have you never seen dried yellow piss on the seat? Last time someone shit on the seat, was it disinfected properly or was it just wiped hard? You ever sniff a toilet seat? If you said "ew gross" then doesn't that imply it's not clean?
I find the waxy paper covers wasteful and annoying, so I just use a pair of 3 paper squares and say "good enough" after a 2 square wipe of the seat for various tinkles and hairs.