Everybody has internalized the idea that if you ask for twice what you really want, meeting in the middle will give you the thing you actually wanted. So if you notice that the other side is doing the same thing, you double it again...
They never read Never Split The Difference. Negotiations are supposed to be value based and each side should listen to the true concerns of the other.
That said, I don't think the political sides are really asking for twice what they want. It seems very clear on most subjects that they really do want all that they are asking for, but will occasionally accept less and continuing to press for the rest in the long run.
Thinking about it, I think you're right that the political sides aren't doing that. The Culture-War wedge issues that are the most polarizing don't really have a halfway; we've seen that with abortion, for example, for decades. All the halfway positions are unsatisfying to everyone, and the issue is still there.
