That's your example of a guy who diffused hyper partisan identity politics? The guy who was so feared by big believers in hyper partisan identity politics (in this case, denying people of a certain identity human rights and keeping them as chattel) started a civil war and then later was shot in the head by those same hyperpartisan dickheads after he'd won the war?
I'm pretty sure just because of the way half the fucking country responded to his election, he's probably the most divisive president in the history of the US. The way the US responded after his assassination and the way the confederacy aristocrats were rehabilitated and happily welcomed back into their positions of status and power in that period of "reconstruction" are probably the biggest reason US politics are a mix of idiotic hyperpartisanship and culture wars.
I think what America actually needs is someone who's an actual unifier. Look at FDR, he came to power because of the corruption and ineptitude of his predecessors leading to what was a total economic collapse. And even then... he was only really able to properly "unify" the US once it was pulled into WW2. But he ended up being one of the most popular presidents of all time because he challenged the status quo... and he was able to navigate the US through it's economic woes (although that's primarily because the US had the advantage of being the only industrialised western nation to not be war torn by the war).
There's no easy fix for Americas problems. It's either going to have to get a hell of a lot worse (total economic collapse, world war, something like that) or America's just going to fall apart due to the media and politicians creating a narrative that Americans shouldn't work together or like each other because of various idiotic political reasons and the culture wars they are pushing. But corporate media has found that pushing culture wars and hyperpartisanship is more profitable than having a fully functioning democracy, and until that changes... that's likely going to be America's future.