Foaming makes the most sense when you mix the soap with an APC to strip the paint.
For maintenance washes, I am sure there is minimal benefit but given how cheap soap really is (only takes 1 to 2 ounces) it is nice entertainment.
However, if one pre-rinses with water, then foams but does not remove, does this make the initial wash mitt contact safer? Or, go to the extra step to rinse, foam, rinse, re-foam, not rinse, and then proceed with your favorite wash method (1,2,3 3 buckets). Of course, if you have issues with soap drying on paint, this is a problem.
For me with a foam cannon, you could use 3 ounces soap in the foam cannon and another 1.5 ounces in the bucket so 4.5 ounces or about $1.50 in soap.