Here, we are cleaning some brick at the Presidio in San Francisco using a garden hose. No chemicals, no pressure, only water. Moderately pressurized water applied to the surface effectively removes instances of atmospheric carbon and soiling. In this case, it may have been the lesser of two evils, since the original mortar between the bricks was poorly washed beach sand and lime mortar. Any excessive water pressure would have blown away the original mortar. This was probably the optimum cleaning solution unless the owners were willing to remove and replace the outer 3/4" of all the original pointing mortar. From a strict Historic Preservation point of view, this would be less than optimum.
Water is a surprisingly effective alternative to many cleaning situations and substrates, but testing is always critical to determine whether the principle of the "gentlest means possible' may be used. There are certainly environmental advantages to avoiding the use of chemicals in the cleaning process.