Three Hours to Pay the Bill
In the mid-1990's I was living at a fellow Canadian's rented house on a Gang between Jl.Sudirman and Jl.Rasuna Said. When he had a pembantu she was always sent to pay the hydro bill, but one time I had to do it.
The PLN office was nowhere near the house ... I think it was in the eastern part of West Jakarta, about 30 minutes by taxi (not macet). On arrival it was a typical 2- or 3-storey whitewashed functional government building, and I queued up outside on the 2nd floor (with all the drivers and pembantus, I assume - in any case the time was passed chatting as I could and answering 'hello mister'

. I was probably 50th in line, outside on the sunny balcony (AC?? it's called sweat!) and recall waiting an hour or so until the wicket opened.
As with you, someone came and took the big Orang Putih closer to the beginning of the line to pay - no one complained. Money exchanged, stamps liberally and vigorously applied to the rekening, salamat jalan's were said, and 10 minutes after the window opened I was on my way.
Another day in paradise!