William, plenty of rug cleaners over here and more so in the USA will all clean rugs using that sort of method. However, in the west we have tended to go overloaded on the technology side of things, compared to the traditional ways used in the countries where rugs originate from. We've got all sorts of things like power washers, centrifuges, masses of expensive mechanical kit....
The traditional Turkish way I believe is olive soap. People do it for themselves, rub the rugs over in olive soap and either wash it out in the nearest available clean water source, or hang it over something in the rain to wash off. Like you say, dry in unbelievable time in that climate.