Speed restrictions, grade crossings without transit priority, poor terminal dispatching, and highly variable dwell times (due to front door only boarding, cash and ticket payment, narrow platforms, and a very slow method of boarding passengers with wheelchairs) cause massive bunching on the branch lines. The Central Subway can't work well without reliable branch lines feeding it. Garbage in, garbage out. The new fare system (arriving 2019) will allow all-door boarding and tap-only at all times, which will help. But a substantial investment - combined with political will that simply isn't there - is needed to improve maintenance standards, modernize platforms, and add real signal priority to intersections.
There is no single bottleneck in the Central Subway, other than that 40 trains per hour per direction is approximately the limit for human-driven light rail. Some modifications - allowing through moves from the eastbound fence track at Park, making the North Station turnback less inefficient, computer-controlled priority at Copley Junction - would reduce delays and make operations smoother. While full PTC would likely reduce TPH slightly through the subway (though better branch operations, and possibly converting the D to all triples at rush hour, would wholly mitigate that), some better signalling and control may also help.
Oh, and having enough fleet to actually run service. The Green Line currently has 164 cars active, of which about 152 are available for service on any given day. 146 are needed just to run the schedule, never mind substantial delays: if there's any kind of slowdown, they outright run out of cars.