I've been doing it for years. IMO, HP soap is just show with virtually no cleaning ability. I have used one BB soap (can't remember the name) that didn't foam very well under HP, but overall it's been pretty much a non issue.
HP Soap is not a great way to get the grime off the car. Case in point is that I have yet to see a Touchless Automatic use HP soap. However, in my SS bays I use the KleenTrack 2A (Simoniz) and it does do an OK job (as opposed to the last soaps I was using that did nothing). It has a clean smell and foams well for a good show. Also, it's inexpensive...about $6 a gallon (so less than my foam brush soap)
I use Scotch Plaid's Red Hot powdered bay soap, and pour it on thick. I'll agree to an extent that the HP soap doesn't need to be good enough to get a car completely clean without brushing, but the customers who come in three or four times a week (of which I have a lot) who just soap, wax and spot-free should be as satisfied as the ones who come in once a month and use all the functions.
I use the same hi-pH presoak for the bays and the touchless auto. It's mild enough that it won't burn paint or irritate skin even right out of the barrel.
Been using KR cherry Blossom foam brush soap and mix in a little triple foam polish, mixed in a 30 gallon drum, 5 gal. soap to 15 water then hydromind to desired foam brush thickness and a draw line with a tip to desired show for hp soap. can color for seasons with different triple colors. Good show and great smell.