For one - a trip from Burlington to Boston takes 3.5 hours by car and 4.5 hours by bus. Unless you can construct a train that runs the trip is 5 or less hours, no one will ride it. Even five hours would be pushing it for it to be popular.
Has there ever been a good study done of the best travel time that can be reasonably achieved going from Bellows Falls to Rutland to downtown Burlington, vs Bellows Falls to White River Junction to downtown Burlington, with some reasonably plausible set of track upgrades?
Essex Junction to Bellows Falls is 133 miles, according to the Amtrak System Timetable. I believe you've said Essex Junction to the downtown Burlington Union Station is another 7, which makes 140 miles.
Google Maps seems to think the highway mileage from Burlington to Rutland is about 67 miles on US-7, and from Rutland to Bellows Falls is about 50 miles on VT-103. That's only 117 miles, about 23 miles shorter than the route via White River junction. Switching to the route via Rutland might cut out a half hour unless the curves are much worse via Rutland than via White River Junction.
The numbers I can find on the web discussing the Ethan Allen extension to Burlington suggest 1:30 or 1:40 travel time on that segment, but don't seem to have clear references to any formal study. But that's also based upon a 59 MPH speed limit; are there straight sections of track that could go faster with an investment in a signal system?
Brattleboro to Bellows Falls is 35 minutes, 24 miles. Can that be improved?
Brattleboro to Fitchburg looks like it's probably 60-65 track miles, judging from various highway routings between those places.
117 + 24 + 65 miles would be about 206 miles from Burlington to Fitchburg. A Fitchburg to Boston North Station commuter train that skips some but not all of the current commuter stops should be under an hour within a few years, and I suspect that could translate to an Amtrak train that stops only at North Station, Porter, Fitchburg, and maybe one other commuter stop covering North Station to Fitchburg in 45 minutes. The interesting question, then, is whether it's possible to get the average speed from Fitchburg to Burlington via Rutland up to about 50 MPH (and I suspect overcoming the slowdown from the curves requires being able to go at least 79 MPH on most of the straighter parts of the route, and might even require something closer to 110 MPH).
The other interesting question there is whether the Boston to Fitchburg tracks could ever hope to support more than the 80 MPH currently planned there. I believe they are planning to upgrade to cab signals over the course of the next two years or so. On the other hand, I believe the typical MBTA coaches and locomotives can support 88 MPH, which suggests that rolling stock limitations are not the limiting factor for speed on that line.