I believe that when washing demineralised water is supposed to be used, which doubtless contributes to the costs involved.
Among other causes of the dirt is de-icing fluid, a somewhat sticky substance which gets all over the airframe and which dirt then clings to, and which impairs the aerodynamic efficiency of the aircraft and leads to extra drag and fuel burn.
On a smaller scale anyone who has operated out of grass airfields in the winter will be well aware of all the mud and grass thrown up onto the underside of aircraft. That certainly does not come off as you potter through the air, clear of cloud, at 105 kts !