If a member of the public wants a priest they should look around the town they are in and see if they can spy a building with a big pointy roof. Failing that, look in the phone book. Failing that, try google. There certainly is a reason why certain priests like to parade in public in full clericals and it has very little to do with being available to the general public or "signalling that this man's function is to labour for the Church."

What do you do when you need a doctor, stand on a street corner hoping that one will pass by, identifiable by the stethoscope sticking out his jacket pocket?