I did look into getting a false beard and matching wig once, out of curiosity. Easy to get a cheap polyester one for fancy dress parties and so forth, but surprisingly difficult and expensive to get one that looks real. They must be available for actors, but where can Joe Public actually buy one?
It could be rather handy for a punter's kitbag. Your mother-in-law is standing in the street chatting to a friend a few yards from the WG's door? Nip into an alleyway, come out a minute later as a different person, and walk past her on your way in.
And how many movies have you seen where the hero is being chased all over town by the police, or the bad guys, or whatever - but he never just pops into a public toilet and comes out looking completely different?