*then

Quite often people don't vote for their own self-interest because they believe in a greater good or a larger principle. This is a good thing.

elected representatives aren't perfectly rational robots that take in each of their constituents' inputs into a fancy weighted matrix and produce a vote accordingly and without concern for anything else. in fact, a big issue is that upon assuming office one's priorities can (and often do) immediately shift so far as to essentially ignore whatever was promised while campaigning - there aren't exactly contracts or anything. it's not uncommon to just blatantly lie about what you'll (not) do then do it, especially if maintaining/increasing power level is on your list.

a better analogy would be something like: your options are ordering one of a few dubious multi-year long supplies of food [politicians] from a couple of entrenched vendors [parties], without any real assurances of what's under the covers [promises, etc.], and with a hefty dose of marketing and falsehoods surrounding all of them [us vs. them, tribal stuff]. or trying to do it all yourself [run for office yourself], which is a huge undertaking and draws ire/counter efforts from all the established players.

The U.S. presidency and Congress are elected via a majority vote, not unanimous vote.

Look into public choice theory. Some voters even see an advantage in incompetent government, in the sense that they think paralysis will preserve a status quo and this is more productive of stability than well-intentioned change that may ultimately go in the wrong direction. It even kinda works as long as you don't have any external shocks; the US has maintained a very long economic expansion (at least on paper) despite a longish period of divided government that has resulted in relatively little getting done.

Of course when an external shock does hit an incompetent or paralyzed government the results can be catastrophic, as we're seeing now.