Cutting revenue doesn't make Amtrak better. It makes it worse!
And again, since no Amtrak train can even get above 25 MPH between South Station and Back Bay there is no point to cutting the station. Again, it's not like your taking the train down from 150 MPH to a dead stop. The train is barely moving when it gets to Back Bay. And going north, the trains will still have to slow down before Back Bay in order to be going the correct speed to negotiate the curve into South Station.
So cutting Back Bay at most would save 2 minutes running time. You don't sacrifice 450,000 people to save 2 minutes. If it were 20 minutes, maybe you'd have think about it.
And Back Bay provides the direct link to North Station via the Orange line, so cutting it would make transfers to the Downeaster that much harder, at least until you come up with the $20 Billion or so to build your tunnel. Back Bay is also a hotel Meca, so for tourists it is a much better stop than South Station is.
Next, Back Bay is already a huge stop for the MBTA, they don't need a reason to make it busier. And they don't need to sit in that station longer to board Amtrak passengers bound to South Station, since they're tying up the mainline tracks and preventing Amtrak trains from getting to South Station.
Moving on, no one in their right mind is going to pay Amtrak prices if they can use a T commuter line, except maybe for those looking for an express ride to Providence. And they're going to board Amtrak no matter what. But I frequently ride the corridor to Boston and I can assure you that most passengers getting on at BBY aren't going to Providence, they are going further down the line. Forcing them to ride over to South Station is just a waste of everyone's time & money. Amtrak gains nothing by skipping that stop and it loses millions if it does!
Finally, cutting Back Bay in no way shape or form is going to do anything to help get Amtrak service into San Fran or Phoenix. You'd lose more money than you could ever save by cutting BBY, making it that much harder for Amtrak to ever try to get into those cities you've mentioned.
FORGET BACK BAY! It's not a problem; it's profit center for Amtrak. Cutting it only hurts Amtrak!