What I think...
A commercial dish machine, like the one used in the place where I'm employed as a dishwasher at (55+ country club w/ private restaurant), takes about 2 minutes or less. Plus, as
@me stated, food soils do indeed have to be rinsed and scrubbed off by hand before running them through the machine. So, I'm imagining a professional kitchen, but on a larger scale, filled with a bunch of commercial dish machines (with no other kitchen equipment, of course).
These machines do not dry dishes, though, which is the primary reason why they wash significantly faster than household models. Plus, they need space in order for the user to slide the clean racks out of. This would really cut down on the space for multiple dishwashers in a row.
I don't mind doing dishes by hand, since it was done in my house for nearly 5 years. At my old house, after our original Kenmore DW leaked wash water all over the floor in late 2011, we swore off using the machine any longer and made the transition to hand washing. It was generally team-based: either my mom (later divorced) or sister would wash the dishes, and then I would wipe them off before putting them away. Doing the washing and drying all by myself would take much longer, though. The long-awaited new DW (Samsung) didn't come until fall 2016, shortly after my stepmom moved in with us. Better late than never, I suppose.
Because my own mother was so obstinate about buying a new dishwasher during this time period, a dishomat would've been a huge boon for my family. However, this is how I imagine what the whole process would consist of: 1) haul our dirty dishes to the car in crates, 2) drive to the dishomat, 3) bring the dishes inside the building, 4) pay to enable the machines to wash dishes, 5) haul the clean dishes BACK to the car in the same crates, 6) drive home and finally, 7) bring the dishes inside the house and put them away. That is simply too much money, gas and labor for me.
So, the net result of a dishomat just sounds very expensive and labor-intensive in my book. It does sound neat on paper, though.