I would think that washing your face, lathering and shaving (X-passes) would more than "clean" your face. I don't know that another lathering would do anything more. The alum is a good idea if you need that. I like to finish with a cold water rinse, dry, witch hazel splash (added benefits of astringent for cleaning & healing) and then some ASB if I need soothing and moisturizing. If I don't need the extra TLC I just go with AS splash. Of course, if you wife likes your routine and the way you smell at bedtime you probably should stick with what works!
"Look Sharp... Feel Sharp... Be Sharp!" TOFLAC-U, BOTSS, SSB, Order of Pinaud