Much as I like your argument here I'd like to point out that there's a central flaw to your reasoning:

You assume that if Italy hadn't been around Hitler would have allocated the surplus wisely, according to what seems rational to you in hindsight.

In reality we can't be quite certain how he would have allocated those soldiers. Clearly at the start, at least, he believed that the number he was sending to each task was sufficient to accomplish his aims. He may have gotten locked down later and regretted it, but you're postulating a situation where Italy is out of the picture entirely, not one where it magically vanishes midway through the war when Hitler would have known his error and would have wanted to use those troops to patch up his bad decisions elsewhere.

So, the real question would be, what would happen if you gave Hitler a "new beginning" --one without Italy, but one with the same lack of knowledge about how the war would unfold, and with the same surplus that seemed so apparent to him?

It's entirely likely he would have just made a different set of foolish and ideologically motivated decisions, allocating his perceived surplus elsewhere. Of course we can't know for sure whether he would have done that, or whether it would have trapped him, or anything else--because it's all purely hypothetical. But character holds true and as somebody else pointed out, Hitler's strong point was his rhetoric and his charisma, not his tactical mind.

That being said, based on what you've laid out here, I agree with you very much that Italy was a massive weak point in Hitler's war. I just am not convinced that he would have been strong if Italy was out of the picture--it seems to me that he could just as easily have developed a different weak point.