The last company I hired to clean my carpeting used the setup you mention. They had three tanks in the van, one for water, one for chems, and one for grey water. I think the tanks were about 100 gallons each, maybe a little less. The truck engine heated the water, to 180 degrees, provided the pressure to apply the chems and water, AND provided the power for the vacuuming up of the water.
The guy said they had a fleet of 25 trucks outfitted that way, and each setup cost 30 grand.
That's a big investment, but....ya gotta spend money to make money, so.........
However, the carpet guys were done in about 30 minutes, which isn't much, compared to the hours we typically use our equipment on the average job.