It may be that no one monitoring 126.7 will have any clue where Butthole is.
I think anybody in the circuit area of an aerodrome not marked on a chart who is monitoring 126.7 by definition knows where their Butthole is...
When the pilot who called in the circuit at Butthole fails to [blah, blah, waffle...]
You are going to build a communication system based on the circumstance of that fantastic and unusual beast? An unmarked aerodrome within ATC VHF coverage at circuit altitude? Sub optimal.
There was a time when a troop of workers, of which I was a proud one, did exactly that, listened to and logged traffic in the circuit, then regurgitated it to the other customers. It was called Flight Service, it was brilliant, but it was not efficient and it is gone. You are advocating to bring it back???