Kenazfilan - the Bose 901 was a huge marketplace success at the time we were developing our initial ideas and prototypes. Audiophiles and specialty stores nearly universally rejected them as gimmicks, but there were some valid ideas in there. The crossoverless multiple driver does preserve phase relationships, which are only partially obscured by the small differences in distance to the reflecting walls. The short distance between the speaker and wall minimizes the distance difference between the reflected wavefront and front-firing direct radiator. The equalizer does not introduce phase shift and the sealed bass rolls off at 12dB / octave, which is quite benign. I concur with your speculation that the design might sound like hash with higher order crossovers introducing baked in phase shifts.
I would love to see impulse response and other "normal" tests on the 901.It might fare fairly well at low levels in a highly damped room. But, those CTS drivers were driven far beyond their linear excursion and the dust-cap "tweeter" was very ragged, and the room perimeter drive is inherently problematic and so forth and so on. I am amazed at their success. Bose spent more on advertising than on product. And it worked for them.
The 901 was, I believe, the only speaker that Jim dissected to see how other designs coped with the intrinsic constraints and trade-offs of the art. It definitely served as encouragement that we could do better.