No, you're right - if the VP could always arbitrarily select other slates of votes, why wouldn't he just opt to stay in power? But as you noted, those challenging slates set in motion the process by which VP's authority comes in to play. And there are many other checks on his power too so I don't think anyone (thinking rationally) believes the founders made the VP have dictator-like power over the election.
I don't have a citation, I apologize. But I believe the authority given to the President of the Senate in this situation is not derived directly from the 12th amendment. He brings that authority to the table because of the 12th A, but is given that authority elsewhere.
It's like the VP has the authority to make the deciding vote on a 50/50 split Senate. The VP has executive authority in certain situation.
The key circumstance is the dueling EC votes. The 12 A requires VP to count "certificates". And he does have the plenary power to dismiss either or both slates.
Its not stupid to see how that can result in a Trump win. There is a purpose for this counting duty of the VP and the authority placed upon him; it's not just a ceremonial act.
I think the assertion of VP having "plenary power" to select the president is misleading.
But the President of the Senate is not just called upon to tally up "certified" votes. The VP does have plenary power to decide what are "certificates" in so doing his duty to count the votes. Since there are dueling slates of electoral votes, VP can decide that the state has not concluded their general election sufficiently. And then things get very interesting.
Or tell them you can't hear them because you have to read lips. "So imagine how much more difficult my life is now..."