Boeings did run on the E, just not that long. Most often they were turned at Brigham Circle but I do understand they would occasionally run to Heath Street. Of course they never operated in regular service to Arborway. Allegedly there was some fear that if involved in an accident with a car, underfloor high voltage cabinets could be compromised, so the T was hinky about operating them in mixed traffic. I cannot vouch for the veracity of that allegation; the theory came from an old thread here on this forum, toward the bottom of the page:
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Certainly MUNI never had such qualms, and even the T shuttled Boeings up and down Chestnut Hill Avenue between the B and C lines and around the loop in the street at Cleveland Circle on a daily basis without issue. My suspicion is it may have had more to do with the 1980s MBTA mentality, when they had just "temporarily" suspended Arborway and exhibited very little desire to operate the E beyond Brigham Circle at all. Any excuse they could make against operating streetcars in mixed traffic was a good one at the time.
For six years in the 1990s I was a near-daily E rider, while I was at Northeastern and later lived on Mission Hill above Heath Street Loop. Once in a great while I'd see a Boeing on the E, but it was truly a "WTH?" moment, and as far as I could discern these rare Boeing appearances always turned at Brigham Circle. I never personally saw, rode, or photographed a Boeing beyond Brigham Circle during that time.