Most of the trips on the Downeaster will probably always originate or terminate near Boston, or north of it. Trains that ran through from south of Boston might pick up through passengers from, say, Providence headed for Maine, or New Haven headed for Durham, but not many New Yorkers would ride to Bath or whatever. Most intercity passenger trips are what, 2 or 3 hours? And even with trains starting at North Station, Greater Boston has plenty of folks to ride to Freeport to shop, Rockland on vacation, etc.
But while we're daydreaming--isn't it fun?--here are some of my favorite ideas about cross-Boston service.
Problems with the N'S rail link:
Huge cost, like enough to make the Downeaster free for ten years.
Trains would have to stop a long way below North and South Stations, so if many trains ran through the existing tracks, platforms, and concourses would be obsolete. (To get down below the highway, the subways, the Charles River, etc., on a reasonable grade, they'd have to start going down what, a mile or more south of South Station/north of North Station.)
Huge cotst, like enough to eliminate a dozen of the worst grade crossings in NE.
South Side delays and North Side delays would become one big, and more frequent, delay.
Good things about it:
Ability to get across town. South-Side commuter rail access to jobs near North Station and vice versa.
Potential one-seat ride from Mystic to Durham or whatever (but since this is a much, much smaller number of passengers than the commuter rail trains, building any N-S link for intercity travel doesn't make sense).
Alternatives:
1. Use the space saved for the N-S rail link for a new subway line instead. If the geography works out right, make it a branch of the Silver Line or the Green Line. Make the walk from the Amtrak platform to the new line's platform as easy as possible, and include special cars with luggage racks.
OR
2. Put the Grand Junction 20 feet underground. Build a bike path or light rail on top, creating a great improvement for that part of Cambridge and getting local pols on your side. Set the underground track up for passenger service at a decent speed. Run trains to Maine NYC-Dorchester Branch-Back Bay-Anderson TC-Maine. Skip North and South Stations entirely. (Trains NYC-Maine used to bypass Boston entirely.) Change to Diesels at New Haven as if train were going to Springfield. This would probably cost a hell of a lot less than the downtown link, which would be deeper and more complicated. It wouldn't do much for commuter rail, though.
OR
3. Renovate Back Bay station slightly to make transfers between Amtrak-Commuter Rail and the Orange Line easier. For example, put in lots of elevators. Build a platform between the Northbound Orange Line track and the nearest Commuter rail track, with a fence and turnstiles, to allow cross-platform transfers; rearrange operations so that Northbound corridor trains and commuter rail trains use that track. Etc.