1922 is hardly 'always.' A little historical context. For over 200 years, 'Boston' was that land north of today's Arlington street. Beyond there was the Back Bay and South Cove. There were two bridges, one to Lechmere Point, and one running towards Cambridge center, which was in the Harvard Square area. Any other bridge to Cambridge would make no sense.
Well after the Back Bay had been filled in, the possibility of another bridge was floated. The third bridge made no sense until Cambridge had filled in its Charles river wetlands, which extended in to Brookline st (Central square). When Cambridge finally did fill in its shoreline, then there was a reason for a bridge - primarily for Cambridge. For Boston, there was little advantage. Boston was eventually convinced when the Boston & Albany railroad tracks were dealt with as part of the bargain.
By the time of the 1922 discussion linked to above, MIT was across the river, and there was no main road on the Cambridge side to connect to. All in all, it just wasn't a very good idea. Running the bridge from West Chester Park/Mass ave. put through traffic at the very edge of the Back Bay residential district. A similar road/bridge connection at Dartmouth would have pulled through traffic into the heart of the residential district - hardly an attraction for residents.
Both West Chester and Dartmouth sts were planed with grass islands. I suspect that was simply to break up the grid, and had nothing to do with bridges. If you look at a map, you'll see that a bridge running straight from Dartmouth street would have reached Cambridge exactly where the Cambridge street bridge already did. It's hard to imagine that was the intention of those who drew Dartmouth st. with the island running down its length.
A little historical context: I've spent the last six years of my life academically studying the back bay.
1922 was the first online reference I could easily link to as a citation for evidence of the bridges planning. The width of Dartmouth Street is directly attributed to the idea of a bridge in that location.
Having the bridge land in the same location as what we now know as the Longfellow makes a lot of scene if you look at the development of Cambridge at the time the Back Bay was being filled. The area around Kendall Square was already somewhat built out due to the access to Boston as well as the intersection of Main, Third and Broadway. By contrast, the area where the West Chester Park bridge would have landed was still a tidal swamp, all the way up to the south end of Central Square, as you mention. Draw a line on a map, it is a straight shot on Dartmouth into the heart of Kendall.
Traffic across the bridge and onto Cambridge St in Boston was already bad at this point, I imagine the new bridge was planned as a relief valve, as well as a way to add to the prestige of the new Back Bay; Copley Square would be the receiver of one of three Charles River crossings (I'm not counting the bridges further up, basically the boonies at this point). Having important things happening in the Back Bay was important at the time, it is no accident that so many schools, museums and churches moved there as the bay was being filled: they were lured there by the city to entice developers to build luxury housing befitting the new neighborhood they were attempting to create.
The civil war really set back the back bay being filled in. Then the panic of 1873 and a whole slew of other recessions and minor wars. Just as the filling and building was finally wrapping up, WWI hit. By the time the Dartmouth Street bridge plans were dusted off in the 20s, the esplanade had already been built out, Cambridge Street had been widened to accommodate the traffic coming over from Cambridge, and the idea for a unified "Massachusetts Avenue" began to take hold.
So yes, there was
always a plan for a bridge at Dartmouth Street. Evidence, citations aside, exist in the continuity of the street though the South End, its width in the Back Bay, its connectivity in Copley Square, and its direct alignment to the intersection of the three major streets in Cambridge.