People have done it both ways and have gotten good results. I may have stated this before in the thread. I was following the recipe by Charlie Papazian. I think the primary reason is for absolute clarity, getting the beer off the spent yeast then give the remaining yeast some scrub work to remove complex starches from the corn. One could also mash with this....

That said, at the end you want dry beer. So mash with AE, mash lower like 147F, use AE in the fermenters. You probably could skip the secondary if you let it stay in the primary for 3 weeks. Another point here to note is the use of 6-Row malt. This malt has more enzymes for use with adjuncts, so bumping the ratio of 6-row to 2-row is another option. Making a dry beer without lagering on ale yeast, AE happens to be cheap easy alternative (aside from altering the grain bill). Think of the act of lagering, slow gradual chugging of yeast to consume any resemblance of food to survive in a cold environment. In this case with the 2ndary you are doing it at room temp with an artificial boost to convert starches into sugars and letting residual yeast consume new found food.

I personally like my kegged beer without any form of yeast (based on the style of course). I don't like having a spent keg spurting yeast sediment into my faucets. I also tend to siphon to the bottom of the fermenter, inevitably I pick up some yeast, so this one I just do the 2ndary without much thought on the matter, but only on this beer style.

If the AE is not working in the 2ndary I would make sure that on future batches that the yeast is rehydrated in warm water prior to pitching. Rehydrate at 90-95F. If that is not doing it then enzyme might be bad.

My $0.02