Alongside the various other problems with pining away for a third party president representing the “radical center” and not beholden to special interests, I do have to wonder what problem this is supposed to solve. Imagine replacing Barack Obama with a hypothetical non-party president, who we’ll posit is to the right of the actual President Obama and also utterly free of interest group ties. How does that get us closer to a bipartisan agreement on the debt ceiling? It’s still the case that you need Democrats and Republicans in Congress to agree if you want to pass something. So you’re in the same boat.
The main difference, as far as I can see, is that getting executive branch nominees confirmed would be much more difficult for a nonpartisan president. Essentially every nominee would be greeted with overwhelming hostility from all quarters as Senators seek leverage points to influence executive branch policy. The only reasonable course of action would be to form some kind of enduring relationship with one party or another and its base of constituency groups. Otherwise how are you supposed to govern?
America’s political parties are entrenched precisely because getting major political change is hard. To circumvent them both effectively, you’d have to do all the work of replicating an entire national political party not just elect a president (as the Republicans did in the 1850s). But at that point, you also might just work inside one party or the other. I suspect that what a lot of people who think they’re not happy with the current two parties are really unhappy with is some mix of “the voters don’t agree with my views” and “American political institutions are poorly designed.” I sympathize with both of those concerns. I wish more voters agreed with me about more things, and I also wish our institutions were less prone to gridlock. But just having some different person sit in the White House wouldn’t do anything to change the fact that bipartisan agreement is both hard to achieve and necessary to enact major change.