That assumes a model where most of the electorate is politically moderate. A sort of "normal distribution" where the mean is centered around centrism. These days, the US electorate is highly polarized and the parties are responding in kind.

This. The result is what I call the democratic (small d) wobble. Each party gives just enough to win (in their judgement) and the independents choose.

The result is a wobble left for awhile, then a wobble right.

A bunch of models I've seen suggest that from 2016 onwards negative polarisation means that it's turnout of each side's base, not independents, that's deciding elections now.

However the resulting wobbling isn't much different in practice outcome-wise so far because turnout tends to depend on level of outrage which depends on how long the other side's been in power, it's had much more significant of an effect on how elections need to be fought.

(much information about this can be found by googling 'negative partisanship' or 'rachel bitecofer' +/- the word 'model', I'm not including specific links because which outlets/articles/etc. will be preferable to a given reader will likely vary so providing a guide to finding a range to select from seems more useful than my trying to select on others' behalf)

They don't have to be in the center, they just have to make the lesser-evil argument. They just need to express to the swing voters that the other party is even more extreme.

In theory perhaps, but in practice it turns out that casting a clear distinction from the other party drives turnout.