They have a budget - but it is not driven by law (like a hard salary cap) ... it is not driven by affordability (nobody is going to be skipping meals) ... it is driven by how much some very rich people want to put into their plaything. I recognize the constraints you have noted - constraints which the Red Sox have chosen. I also recognize that those constraints are entirely voluntary - and thus have relatively low patience for rationalizations in that direction.
I respect that the Red Sox have put a ton of money into the club and the park. Given the prices they charge and the numerous monetizing opportunities they have exploited, it's the least they can do.
Now someone called baseball an odd duck as a business - that is because it is a business, but to the owners, it is essentially akin to owning a piece of valuable art. It provides status, it feels cool to own something you like, and you will make a killing whenever you choose to sell it.