Watch out for mj. He claims that 5/3/1 is the pinnacle of training. But we all know that his success is from eating all those who don't worship at the altar of 5/3/1.
I agree with you on the overtraining aspect. There is no way that I could do multiple 5x5s, of major compound movements, in the same workout, multiple times a week. When the weights are light, maybe. But not once I am really having to put effort into it.
I guess you could try 2 workouts a week, and get more recovery. But I need to workout 3 days a week. 2 times just isn't enough, even if only psychologically. 4 times has proven, time and again, to be too much.
They claim that the 1x5 on deads is just because it would be too much to 5x5 squats AND deads multiple times in the same week. To get around that, though, you could 5x5 the deads and 1x5 the squats.
I do a bastardized 5x5. And I only use it on upper body.
Saturday- Bench 5x5 + back work (not 5x5, unless on a whim)
Monday - Deadlift for heavy singles, doubles or triples. Sets of 5 at weight kill my back. With my issues, it is just too much. Squats aggravate my back more than deads. Since I have a real issue with my back, I just skip squats.
Wednesday - Military Press 5x5 + BB shrugs and DB work (not 5x5)
So far it has yielded results. I had never been able to get more than 3x5 @ 300# on bench. I hit my 5x5 on Saturday. Also, I had never been able to get more than 3x5 @ 215# on Military. I hit my 5x5 last Wednesday. We'll see how far this can go.