I don't think it's so simple that the richest guy will always outbid the other less rich guy. If JH bid $800M, I'm not sure Cohen goes higher. In that sense, JH chose to bow out.
My point was that even if Cohen wants a few guys JH wants, it does not mean he will treat every bidding war like Soto's. He may think, it's not worth it and pivot to someone else he likes, too. In other words, I don't think it's a done deal on every FA.
Since Cohen got Soto and the Yanks got Fried, I'm not so sure the bidding dynamic will be the same, if the two NY teams are in on Burnes, Bregman, Teoscar, Santander or anyone else the Sox are also bidding on. They both got their prize, and may not feel it is worth it to one up JH on one of these guys.
While it may still be true, if they will never be outbid, eventually JH will drop out, but we don't know if that will apply to every FA 2 or 3 of else teams are seeking. Cohen does have a history of backing off, at times, and the Yanks have been roasted by fans for many years for not going one step further on spending.
I just don't think it's a foregone conclusion we lose every bidding war, going forward. If we do get one, you'll say it's only because the two NY teams didn't really want the guy, and we did not outbid them.