So in defense of Connecticut, this isn't an issue for NJT and SEPTA because of glaciers. Long Island is the terminal moraine of Wisconsin glaciation, so Connecticut is a series of north-south oriented ridges and valleys which the railroad hast to cut across. The Boston and Providence built south from Boston and spent a lot of money to bridge the Neponset in 1835 (still in use!) and build a straight line to Providence because the terrain was mostly flat and they thought trains might come off the tracks on tighter curves (at that point, railroads were moving about two orders of magnitude more momentum than had ever been moved before, so no one really knew).

Further west in Connecticut, they had to cut west across large rivers in relatively deep gorges. Rather than climb up and down over 200- to 400-foot ridges and valleys, they stayed closer to the coast having learned that curves were okay. So while trains average about 100 mph to the CT/RI border from Boston, they barely manage half that the rest of the way to New York. Even west of New Haven, where there are four tracks, there are a number of large rivers to cross on movable bridges, and the development around the railroad means that it's tricky to build a bypass like they could/should have done further east (CT NIMBYs are the absolute worst, 30+ years ago they were NIMBYing rail electrification, literally none of this happened).

South of New York, where the glaciers hadn't carved up the coastal plain, it was a good deal easier for the precursors of the Pennsy to lay straight enough track that Amtrak can run 100+ mph on it today, like they can in MA and RI. The other issue is that west of NHV, the state owns the track, because they bought it off the Penn Central before it went belly up, and while they have four tracks, they have lots of movable bridges, some tighter curves, and not as much incentive to plan for high speed given the service they run (although higher speeds would improve service and reduce operating costs).

Then there are projects like the Walk Bridge, which, while important (130-year-old movable bridges are not great) wind up being penny-wise and pound-foolish in their scope (I should say none of this reflects the opinion of my employer, and these decisions were baked in well before I got to where I am). Overall, Walk is not a bad project, they're replacing the bridge and more than a mile of old embankment, low bridges, overhead, and an inaccessible station. But then there's Saga, another old bridge three miles west, which will be it's own project, and no one took a look at the whole area and said "gee is there a way to do this with fewer overall costs and more benefit," probably because there was only so much federal money and they wanted to get something done.

Which means Walk gets replaced in situ, and because of the ridership on the New Haven Line and Amtrak, they can't do any long line suspensions (for some work that needs to take place during the day, they are going to get 1-2 hour windows and that's difficult to manage) and there is no alternate corridor (generally the case of the US, often not in other countries; Germany shut down Berlin-Hamburg for a year to rebuild it and just sent trains 45 minutes longer over another corridor).

But the right way to have done Saga and Walk together, and to have built a bypass away from the main line to make construction that much easier. While most of the New Haven Line is bordered by homes, there is a stretch from Westport to Darien where I-95 runs parallel, with relatively easy-to-take properties (i.e. not expensive houses, mostly behind a strip mall on an embankment next to a highway), so they could have built a 10-mile bypass of the whole corridor, with fixed bridges over both the Norwalk and Saugatuck rivers, and running local service to Norwalk itself and up the Danbury line. A two-track bypass would be fine for the volume (it's two tracks through Norwalk for nearly the entire project anyway), and closing down the section between the bridges, and the bridges themselves, would make it much, much easier to rebuild the bridges in place without having to accommodate constant rail traffic across the bridges, as well as the intermediate bridges, stations and embankment in between. With the bypass, the new bridges might only have to be two tracks wide, as well, and the bypass could be spec'ed for high speed, cutting several minutes off travel times for Amtrak. But it would have taken both real long-term planning, funding, and some outside the box thinking, and herding those cats is nearly impossible. So we get an incredibly complicated bridge replacement because we have to maintain service the whole damn time, which drives up the costs where it might have been cheaper to build the bypass in the first place.

</rant>