Would they? I'm gonna be cynical here but why would they care? What would the "educated people" do otherwise? Not vote? So what? One of the 2 parties would gain power regardless.

If the populace are better educated, informed, and engaged, then having policies which are more evidence-based than your opponents' is more likely to get a greater vote share. This shifts the direction of the arms race away from senseless posturing and towards actual policy debate.

That's the idea at least, and I think it's worth considering. But yes, speaking as someone looking in to the US from outside, a more proportional voting system would also do wonders for your democratic legitimacy.