Talking about putting your bags under your seat: I heard on the news about one Japanese lady who absolutely refused putting her new Gucci bag under her seat and have gotten in all sorts of trouble with the crew on her plane. I am very sympathetic with her.
didn't she hold the whole plane up for hours and end up being forced to get off the plane? that's just completely insane, if you're that paranoid about your bag you shouldn't be flying commercial. more likely than that you need your head examining if you think your bag is more important than flight safety. if i had been on that plane i certainly wouldn't have been happy to be delayed because i happened to be on the same plane as a complete lunatic.
In Europe, a lot of people carry huge trolley bags on board, and the wheels of those have been everywhere, so there's no way the bins can be clean!
but who puts wheely bags in the bins they usually wouldn't even fit! i don't ever recall seeing a dirty bin, although on a rainy day flying out of london i can see how it would be possible since you have to take your shoes off there.
the furthest i'd go in the name of "bag safety" is putting it into a le pliage, i sometimes do that anyway for the security check with the one bag rule in the uk (which fortunately is only in force for another three or four days ), other than that i think people get far too paranoid.