The main reason was the relocation of the entire station - the modern site off Market Street allowed for the construction of a parking garage and drop-off lane (buses were moved to the dropoff lane in 2002) which wasn't possible in Central Square. The Market Street facility was designed to accommodate a Blue Line extension without major reconstruction of the Commuter Rail side of the station, and the garage was sized for BLX as well. (Remember, this was the early 90s, when BLX looked like a very likely thing).
The old platforms were fairly narrow islands - 20 feet wide in the middle, and narrowed on the ends. You'd have had speed restrictions for passing express trains because the center tracks weren't quite straight, and there's just nowhere near the frequency of traffic that there once was on the line that justified four tracks at the station. (Passing sidings between Lynn and Swampscott, or a BLX-2 to shift Swampscott + Salem State + a lot of Salem demand onto the BL, would be much more useful.) The old-quad-tracked station design was built during the brief era where the New Haven had a controlling interest in the B&M, and was planning a cross-harbor tunnel and complete quad-tracking of the Eastern Route out to the Beverly split. In practice, the outer tracks ends up being used mostly for Saugus and Swampscott Branch trains (neither of which will ever be CR again), and for letting expresses pass locals (more important in the days before bidirectional signalling).