^ Great questions. I'm not an expert, so don't take this as gospel, but here's my understanding...
Blue to Riverside
There is indeed a lot that makes sense about this idea, and 80 years ago it might have been done, in much the same way the current Blue Line and Braintree Branches were old railroads converted to HRT. There are two pretty big challenges, though, that make it less favorable than you might expect.
First, Riverside Yard. This is the Green Line's largest yard and,
as nycsubway.org notes, is where most major repair projects happen. Conversion to HRT pretty much cuts that off from the rest of the LRT network, which makes for a Big Problem. You could maybe possibly work out some sort of "time-share" agreement where LRT vehicles are moved at night to the yard, but that's a whole lot of hassle, and still leaves you vulnerable during the day. And there's basically nowhere else to put a new LRT yard, at least not until/unless you build an extension elsewhere out to 128-land. (Like, maybe you could find some place up in Woburn, but, again, it's a Big Problem to solve.)
The other problem, ironically, is the very extension to Needham you propose. Converting Needham Junction-Needham Heights to LRT and connecting to the Green Line at Newton Highlands has been on the books for 80 years, and has been a serious proposal for most of the last twenty years. In fact, if I had to put money on it, I would bet that Green to Needham will be the next rapid transit extension to open after the current Green Line Extension project to Union Square and Medford Hillside finishes. It's still a good ways off, but it's easily the most reasonable rail extension we ever discuss on here.
The problem is that the corridor in Needham is very LRT-friendly, and very much not HRT-friendly. The big problem is a whole shedload of grade crossings in downtown Needham. Tunneling would be expensive overkill, and an elevated would be also. Unlike the current Riverside Branch, the Needham Branch is not grade-separated, which is basically a requirement for HRT these days. (If you go to Chicago, you can find a few HRT grade crossings, but they are very rare, and pretty much not built anymore, and with good reason.)
So if you to Blue to Riverside, it basically closes the door on rapid-transit-ification of the Needham Branch, which then creates
huge problems for the commuter rail. (The Needham Line really shouldn't be a commuter rail line and it really creates a headache by mixing in with the Providence Line and Franklin Line, etc.)
So, between those two, Blue to Riverside looks much less appealing.
Branch to Needham
As explained, this is very much a thing -- for a Green Line extension.
Infill for Route 9
This is not so much a thing, in this exact form. A new station between Eliot and Newton Highlands would make for extremely close stop-spacing, and it's in a generally residential village area -- not optimal for a park-and-ride.
As part of the various Needham proposals, however, there usually is a proposal for some degree of park-and-ride at Route 128, between Newton and Needham. This would hopefully soak up a bit of the Route 9 traffic.
Likewise, there are perennial proposals to increase service to Riverside via the commuter rail line from Auburndale. (For example, as a branch of the Indigo Line.) With proper transit-oriented development, this could also pull in some more of the traffic from Metro West (although my understanding is that that parking lot is often filled these days -- well, pre-pandemic, at least).
Blue to Huntington
Well, to be fair, TBM'ing under Back Bay is itself pretty challenging. This is what
@JeffDowntown was getting at: Back Bay is built on landfill which makes it seriously complicated to tunnel under. If you aren't familiar with the term -- Back Bay used to literally be a bay of sorts, at the "back" of Boston (which used to end pretty much at the edge of the Public Garden), though "bay" is misleading, as it was more like a marsh. When the Boston & Albany Railroad (today's Worcester Line) was built, it was built along a trestle between what is now Back Bay Station and Allston. This trestle (fun fact) actually was really important in the history of Back Bay because it managed to slow down the water movement from the tides enough to make it feasible to start what we know call "land reclamation" -- basically dumping lots and lots of materials into the marsh to turn it into solid land.
But... the water's still all down there. And all of the buildings in Back Bay were constructed under the assumption that the reclaimed land would stay exactly where it is -- including the water that's mixed in. If you're tunneling down there, and you accidentally drain out some of the water, the reclaimed land will shift, and the buildings will literally crack open. This
actually happened twelve years ago when the T was renovating Copley to make it accessible.
So the TBM part is itself probably crazy enough to make someone think twice.
But, let's say that you get the Blue Line to Huntington somehow. (One option that occasionally gets bandied about -- even as far back as 100 years ago -- is tunneling under Boston Common from Government Center, basically aiming for Park Square at Columbus Avenue.)
Totally agree that Huntington is well-worth a subway. The ridership on the E Line is
nuts. Check out the figures on
page 15 of the 2014 MBTA Blue Book.
Now, as discussed above, running the Blue Line out from Riverway to Brookline Village to Riverside probably is a no-go. However, extending the Huntington Subway from Symphony on out further is definitely something to seriously consider.
In fact, what you describe -- extending the Huntington Subway out to meet with the D Line -- is something we've discussed here a lot and which I think is ultimately one of the best things the T could do to reimagine the Green Line. The D and the E both merit more proper rapid transit than the B and the C -- the D because of its higher speeds and longer distances, and the E because of its ridiculous ridership. It makes sense to join them together. (But, join them together as LRT Green Line, not HRT Blue Line.)
In fact, most of us on here agree that such an extension should go east as well as west -- instead of joining up at Copley, continue east to Back Bay Station, and make your way either along the Pike or in a new subway under Stuart Street, and then join up with the old Tremont Street Subway in order to join the Central Subway at Boylston. That way, you avoid the flat junction at Copley, which often causes delays (and all the moreso if the D and E were joined up), and can leverage the fancy flying junction at Boylston. (But that's all a whole nother story.)
Downtown Capacity
You're totally right that this is a serious consideration. Strictly speaking, an extension to Nubian
might be able to skate by thanks to the loop at Park Street and the quadtracking between Park and Boylston. But it would need careful planning.
I'm a little fuzzy on this, but my understanding is that there is also some signaling infrastructure improvements that could be done to improve capacity in the Central Subway.
The way most of our discussions have gone, the largely emerged consensus is that the way to expand capacity of the Green Line isn't by replacing parts of it with HRT, but instead by adding new "legs" so that the whole system doesn't have to funnel through one tunnel. A typical suggestion is adding an "eastern" leg that connects Boylston and South Station. There are differing versions of this idea, but the general concept is that if you create a second place for Green Line branches to go, you can take some out of Park Street and send them to South Station instead, and thus free up space at Park Street for other branches that aren't well-positioned to go to South Station.
There is a thread called Green Line Reconfiguration that goes through a lot of these ideas, but basically there are two main proposals.
1. Tunnel under Essex Street direct to South Station. This was proposed long ago as an extension to Post Office Square, but we usually talk about sending it to South Station and then the Seaport via the Silver Line tunnel.
2. Go south in the existing abandoned Tremont Subway, hook around when you hit the Mass Pike and head east, and then hook north to enter South Station, basically paralleling the commuter rail tracks, and again head on to the Seaport.
I personally favor Option 1, but that is a very long discussion unto itself.
And, just to bring us full circle, the other major relief for downtown capacity is an extension of the Blue Line to Kenmore, where it can provide express service to transferring passengers. Likewise, the North South Rail Link and the basic Blue-Red Connector would also relieve congestion.