I am never exactly sure what people are trying to argue where profits are concerned. So, what exactly is the argument? The common inference is that because MLB owners are rich that they should be willing to operate at break-even or even a loss. The other inference seems to be that because increases in team valuations have been very high they should be willing to operate at b/e or a loss. I guess the overlying inference is that we could afford elite FAs if only owners were willing to forgo profits. What exactly is the point of constantly point in pointing back at owner's profit?
Well, yes, they should operate the team at break-even. That's what I would do. Wouldn't you?
You are already a billionaire, you can already live whatever lifestyle you want. You have other ventures making money. Beyond keeping a reserve of funds for the team (which yes should probably be enough to operate the team for at least a full year -- heck, 5 years), why not operate the team as a break-even venture? This would zero out your taxes and be a heck of a lot more fun. In the United States, wages are 100% tax deductible.
Isn't sports about having fun? If running a team is a headache, sell the team! If counting beans is what drives you in life, stay in real estate.