I'll go over the actual ridership data at some point, but by far the biggest reason is just capacity. The 39 is one of, if not the busiest bus route, and it is constrained in its capacity by using articulated buses. A 2 car GL train can hold ~3-4x the number of people as an articulated bus.
Quickly commenting on this - this gets into the question of:
Should we LRT-ify every (busy) bus route?
The 39 is hardly unique in ridership and capacity needs. 1, 7, 28, 57, 66, 111 etc all have strong arguments for increasing capacity, and many of them are easier to convert to LRT than the 39. In fact, the 1 and 28 receive frequent calls for LRT conversion among transit enthusiasts
(I disagree with them for reasons unrelated to this comment). You can even throw in some other bus routes with slightly lower ridership, such as 9, 32, 70, 77, etc.
So if you want to do the 39, why not do them all?
And even if you do want to LRT-ify the 39 due to ridership, another option is to run the 39 as a standalone LRT route that does not through-run with the E branch (similar to LRT-ifying the 28 that does not through-run with an F branch to Nubian). In a world with Huntington subway, you can have the heavy-metro lines run in the subway and LRT39 run in street median that's formerly occupied by the E branch, for example.
In terms of transfers though, it seems like there's a huge number of alightings at Brigham Circle, so it seems like people are transferring to the E branch there, rather than riding all the way to Back Bay/Copley.
I'll come back to your earlier comment, but regarding just this part alone, I doubt that's true.
I've personally seen cases at Riverway where a bunch of people were waiting for the 39, but none of them boarded the E when it arrived. For people transferring to GL, I imagine it's better to do so at Copley, where you get all 4 branches instead of just one. And if people only need transfers to the E, the initial BNRD proposal of completely repurposing the T39 from Brigham Circle wouldn't have received nearly the same amount of backlash as it did.
The alightings at Brigham may be explained just as well by the number of people working in LMA, especially since the 39 is one of the few established "LMA feeder" corridors that employees there may be more willing to live in due to the convenience of transit. If anything, transferring to the E at Back of the Hill, Riverway, Mission Park and Fenwood Rd is much more convenient than Brigham Circle.