[Seeker]

I wasn't aware that the suds did anything, I thought it was the detergent part of the shampoo that helped release the dirt and cut the grease. We always associate suds with being cleaner but it just means the water/shampoo mix has been agitated more (imho)
In a warm climate, leaving the suds on means you'll get soap smears.

I see nothing wrong with your technique and if it gets your vehicle clean and you're happy, who cares?

On a slightly related note - the foaming agent (surfactant) they put in hair and body shampoo, some toothpastes etc (possibly car shampoo - I've never checked) is Sodium Lauryl Sulphate and was originally intended to get grease off driveways and it's a skin irritant.