The problem is that there doesn't seem to be a plausible excuse for the wand thing except "Voldemort was careless", and carelessness under such conditions simply hasn't been part of his character at any point until now.

Word of God says that the plot of HPMOR was set in stone since the beginning. If there was some better reason for Harry to face the Final Exam with a wand in his hand, Eliezer would have known about it from the start, and could have seeded all the necessary foreshadowing for it way in advance.