True enough, but the party structure is not established by the constitution at all. There's nothing that mandates the existence of political parties at all.
In fact, these days there are more people that don't vote than people that do, mostly because people have lost faith in the party system. If those people were to form a third party, that party would steamroll both of the existing ones.
And runoff elections are already possible if no candidate wins a majority. There's nothing that says that states can't amend their constitutions to create that dynamic. Some already have it if I'm not mistaken. Adopting that policy alone would allow for the end of two-party dominance. If they had public campaign financing based on which party voters register with, where crossing a certain threshold of registered voters guaranteed an equal portion of campaign funds, it would eliminate special interest control of the election process at the same time.
The opinions aren't the distraction. The refusal to respect the right of someone to disagree with you is the distraction. Having 50 partisan debates allows for the decision to be made locally so that those municipalities can have what they want locally without forcing it on people universally. If you don't like what your state government does, you can move. If you don't like what the federal government does, all you can do is secede or revolt (neither of which are without partisan consequence themselves).
It also allows for the different approaches to succeed or fail on their merits. If people disagree on the best approach to solve a problem, it's valuable to society if all the approaches are allowed to be tried and tested on their merits. If one approach provides better overall results than another, there's no rule that says the state with the inferior approach can't voluntarily adopt another approach after seeing how well it works.
Gay marriage is a pretty good example. With states allowed to adopt the policy on its merits, other states may see that it's not a bad idea after all. Maybe the societies in those states collapse in a heap instead, proving the arguments of the religious right. Who knows until society is allowed to try those things and validate them on their merits, and why try something on the whole country at once when half the people think it's a crappy idea?