There’s nothing wrong with proxying. It only becomes an issue if you’re playing in a tournament, or your opponent insist on using real cardboard since they probably spent a lot and so everyone should as well.
Plot twist: Gordon doesn’t actually need the bat signal to contact him. It’s there to drive fear to street criminals when they see the sign and think that the Bat is heading their way.
Also Gordon prefers talking to the man dressed like a bat on the rooftop rather than in his small office.