I guess the question is, how much easier is this? You are still mashing, still heating your sparge water and still running off x gallons total. The only difference is when you add the sparge water, before or after lautering the first runnings. I'm sure theres a reason thats associated with the system you're using, just wondering.
Also, why recirc for 15min after adding the extra water? What is this supposed to do? Other than a stir to homogenize everything, I'd suppose there would be no reason to wait.