The problem is that in a perfect world zero people would drive to Fenway. There is demand for parking, but it's honestly not helping the neighborhood.
That's plausible at the garden where you've got the entire north side of the commuter rail a metro line and a light rail line. At Fenway all you've got is a single commuter rail station on one line and an overcrowded light rail. Not enough public transportation for the 40k people or so that go to each game.
Plus lots of people are coming in from places outside of 128 where there isn't much public transportation.
Sure getting rid of parking sounds nice, but its never going to happen until cars can drive themselves.