Running it more than once does not change the math at all. It only reduce variance. If you have 20% equity in a $20 pot, then you will collect $4 from that pot on average, regardless how many times you run it. If you have 80% equity in a $20 pot, you will collect $16 on average. And so so and so forth. Apart from reduced variance, which can be good for
bankroll management, the difference is purely psycological.
If you run it once, you either get nothing or $20. And if your long term expectation is $16, then nothing is a big negative deviation. Whereas if your long term expectation is only $4, then nothing is only a small negative deviation, so it dont affect you as much emotionally. You are kind of expecting, that your KK will most likely lose to AA, so when it actually happen, you dont get as emotionally upset about it, as when your AA lose to KK.
Its true, that when you are behind, you will rarely win the entire pot when running it twice. But you will get a decent amount of chops, which is already a good outcome, when you were behind. And reversely when you are ahead, you will rarely lose the entire pot, but you will regularly need to settle for a chop. Which is not a great outcome, when you were a favourite to win.
If you want to use running it twice in a tactical way, then running it only once makes sense, if you think, your opponent will tilt, if they lose, and then also rebuy. And of course that you yourself will not tilt. If on the other hand you think, they will likely leave, if you bust them, and they are a bad player, then by all means run it twice and increase the chance, they will stay and keep playing.