We should be clear that "MLB" refers to the 30 ownership groups as a collective. It is entirely within their power to fix the problem; further redistribute league revenue and create payroll floors such that every team has to have a competitive payroll. I'm pretty sure this would not require MLBPA approval.
But rich people don't get rich by thinking about the collective welfare over own. They get rich by using other people's money to make capital investments that drive growth while ensuring the operating costs that come out of their own pocket stay under control.
So the rich ones won't further subsidize the "poor" ones and the "poor" ones won't spend themselves into an operating deficit (or, in a few cases, risk getting close). The much more palatable solution is use their collective bargaining power to artificially cap their costs. But labor isn't cooperating, so the owners are stuck.
I swear, one of the biggest insights I've gotten in the past few years was from Ezra Klein's book on political polarization: The easiest way to bring lasting peace between two competing parties for them to find a 3rd party to exploit together so they both can "win".
This situation is squarely on Manfred.