What if....?

I had rather hoped that VP Harris would take a radically new approach to being the tie breaking Senate President. Namely, just say, well..... "given the fact that the two parties are tied 50/50, I will simply follow the plain words of the Constitution, and preside over the Senate. All the time. Forget about the "president pro tempore," and organizing rules. I will preside, thank you very much. And you, Senator McConnell, may sit down."

It's never been done before. And, alas, she did not take this step. But I wonder what it would've been like had she done so. She would only vote when there was an actual tie, but as far as I am aware, there is nothing actually stopping her from asserting her constitutional prerogative to preside over the Senate at all times.