How would it make presidential elections less competitive?
It would bring back the interesting dynamic of second, third, fourth, etc. preferences that we used to have in some presidential elections. It would also make our elections slightly more realistic... Unity tickets don't happen in real U.S. elections.
It would make them less competititive by more or less ensuring that people vote for their party. They already do to a large extent and it's only the running mate that tends to make things slightly more interesting. I agree that we need more competitive elections, but this is the wrong way to go about it.