Having the ability to do your own laundry (especially with small kids) is pretty basic.
That's not a given without running the numbers. Whole picture statements like these get complicated in a hurry. Manufacturing 1000 small household washing machines creates jobs and so on.
The work to me seems to be such a big factor in this story that all other things being equal you're going to have to make the case either by ignoring a huge number of factors or you're going to have to go by a model that just focuses on the major component of the operation itself (washing).
Household washing machines last quite a long time (10 years or more), are relatively cheap, maintenance free and two steps away from the point of origin of your washing.
Commercial machines are expensive, require frequent maintenance due to increased use, may or may not be more energy efficient and require trucking around washing.
I don't think you can say that the commercial machines are more efficient due to their reduced number because that may not be where the majority of the expense is located.