Think about it, we wash our hands then open the door which has been opened by a lazy git who hasn't washed his/her hands. If wash basins were outside the room people wouldn't have to touch dirty door handles after washing their hands and people would be shamed into washing their hands as they'd be in full view of other people.
grab paper towels, place under your arm. wash hands, LEAVE WATER RUNNING, dry hands using paper towels, use the same paper towels to turn faucet off, use same paper towels to open door. find recycle bin and throw paper towels away. would rather waste a bit of water than expose myself to some butt-wad's lower region STD germs.
Like M M I try to open the door where fewer people will have handled it. But, I have to say, ladie's toilets are so busy there's generally someone on their way in and you can slip out before the door closes, hence you don't touch it at all.
but mirrors are next to sinks.. and it would feel awkward to adjust yourself outside the bathroom or try and fix your make up or whatever, too when places dont have a push door for leaving the bathroom (that I can kick open, or push with my elbow) then I use a paper towel to open the door and then toss it into the trashcan. If I miss, oh well, cause I don't want to get my hands dirty
I always use paper towels to open doors after using the rest room. Also a lot of places in my area have put hand sanitizers outside their restrooms. But the sinks are in the same area for ease in hooking up water lines.
Probably more to do with convenience, its easier to have all the water pipes running in the same area rather than putting a sink out the way from the rest and spreading water pipes all round the house. I totally see your point though, but I don't think where the sink is would make any difference to anyone disgusting enough not to wash their hands.