A year or so ago now I took my DGS1, then aged about 3½, to the loos in the parent and toddler room at Westfield Stratford, as I knew he would love the fact that there was a gran-sized loo and a boy-sized one, ditto washbasins at relevant heights. Sure enough he did love it - but there was nowhere to dry our hands. "We'll just have to shake!" he said!
I've come across the person handing out paper as you go in, most recently in a station loo in the Czech republic. And one place I went to - forget where now - it was quite expensive, but for your money you got shown in to a private cubicle with the hand-basin there, so you could make yourself clean and comfortable and tidy your hair in decent privacy. Wish there were more like that.
My daughter's worst experience was in New York City, when she and a friend were caught short, so they popped into McDonald's, expecting the nice, clean, tidy loos that McDos have here - only to find that there were no doors on the cubicles!