This doesn't seem right.
First, there are a lot of political systems with more than one "side", and in which coalitions are at least somewhat fluid. This is even true in the United States; if you have ever served on a board that proposes a bond issue or tax increase, you know that that coalitions are quite local and easy to fragment (need to build a new school on the south side, but the north side has lots of tax hawks? Include a new football stadium on the north side as part of the issue).
Second, think about conflict outside of politics. There is a lot of conflict in markets, for example, but most markets do not tend toward duopoly.
I got real fond of saying, "compromise means everybody is equally unhappy with the solution" and giving them solutions that worked but often took each of them a couple extra lines of code. Helping them figure out what those lines were smoothed some feathers, but I don't think any of those people were comfortable unless at least a couple feathers were out of place. It's weird when people 10 years older than you are acting like babies. It's not like 'mature' is the first adjective people would use to describe me at that time. When you don't want to be the adult in the room, it's all the more annoying when you have to be.
Mostly true for political systems that are set up as dual parties. Turns out if you have a system that encourages a more open political ecosystem, there are more "sides" that people can end up on.
that's why starting with the "political spectrum" is bound to give you false information. it compresses too much of the complexity down into a simple model that doesn't predict the world in any meaningful way. it may aid conflict, but that's exactly the trouble: couching sociopolitical challenges purely in terms of conflict itself perpetuates, rather than helps to solve, problems.
and as others have noted, you can just as easily have multiple political coalitions coming together to solve problems without devolving into dualism. humans prefer but don't require binary political stances as you're asserting. moreover, even binary issues won't all fall neatly into a single left-right spectrum without active coercion (which is most of what we see in mediopolitical theater).