On reflection, I find myself kind of awed by Dwight Eisenhower's meta-level thinking. Which is not a thing that I ever expected to find myself saying, I assure you.
Everyone, meaning absolutely everyone, loved him for winning World War II. Both major parties tried to get him to run for president, because he was almost certain to win and he had no discernible ideology tying him to one faction or another. Many people advised him, at that juncture, to go with the Democrats, on the grounds that the GOP was a terrible party for losers. Which was just true, at the time. The Republicans hadn't held the presidency in decades; the Herbert Hoover stink still clung to them; they were generally seen as an organization that mostly catered to rich reactionary cranks.
And Eisenhower, after flirting with the idea of remaining apolitical, decided to become a Republican. Not in spite of the GOP being a terrible party for losers. Because the GOP was a terrible party for losers.
He wasn't ideological, but he did have certain issues that he cared about deeply, such as robust US support for NATO.
He saw that even though the GOP was in the doghouse, it was still a pillar of the American political system; its role in the FPTP system couldn't be evaded, and it couldn't be kept out of power forever.
He saw that any political issue that became a factional issue, a bone of contention between the two big parties, would be a source of perpetual instability. Anything meant to last would require bipartisan supermajoritarian support.
So he went and made the Republican Party what he needed it to be. The Democrats could handle their role in the pageant on their own, but the GOP couldn't.
Any gambit like that would be much harder, these days. No one has been in Eisenhower's position since...Eisenhower.
But it's true that the hyperpolarized world, the world in which the parties are toxoplasmically driven to maximum frothing conflict over literally everything, has not been good for the stable stewarding of anyone's agenda.