A president or prime minister will be the public face of the nation. He'd be expected to meet with foreign dignitaries and speak in public. At the very least, a debate gives people an idea of how their leaders carry themselves when under stress in full public view.

Yeah, that's the argument I was talking about when I said "there is an argument to be made...".

In fact, this is a silly hypothetical because we could have both verbal and written debates.

Making prepared statements is usually done by a politician's staff. The candidate might make some suggestions and approve/reject a draft, but otherwise such a debate would be staffers vs. staffers.

As it should be. Generally speaking, in the type of races I have in mind, politicians don't sit around hammering out policy ideas and details, they get all of that from their staff and other advisers. I feel like it's more important to know how good their team is, and less important to know how good they are at public debate.

My feeling is that like 70% of the value the public gets out of politicians is the quality of their team and how well the politician integrates with that team.