A separate authority might make the service more secure. It would at least mean that an MBTA board dominated by people from Greater Boston wasn't balancing trains west of Worcester against the Lowell Line -- and for that matter the Red Line and the 51 bus -- every time they made a budget. It's not the only way to do that, but it is one way.
A small separate authority could be more efficient than a new office within the T. The board and its meetings won't cost much, and a handful of people in an office in Springfield could manage the western trains more easily than a similar handful of people within the T who had to report to/seek authorization from the T GM, who would always mostly think about Greater Boston transit. And they could all live out in Western Mass, closer to the service they were supervising (less work travel money).
The T and the new authority are/will be creatures of the state, with all their powers and obligations created by state law. The General Court could say that the MBTA must allow x slots at z times at y speeds to trains from the west. It could require the T and the new authority to cooperate on fares, schedules, etc., along overlapping routes, and it could even require the T and the new authority to coordinate equipment purchases: imagine the T and the new authority using at least some compatible DMUs with fully automatic coupling so that a Western Mass DMU (with suitable corridor seating) could come into Worcester and quickly couple onto a waiting T DMU (with suitable commuter seating), and the whole thing could proceed to Boston as skip-stop express, occupying just one slot.