If you have a speaker with a good off axis response you have options. If you absorb the sound at the first reflection you will get more focus but lose some envelopment. In audiophile terms you might get better imaging but lose a wider sound stage. If you have no absorption you get a wider sound stage. With diffusion you often get an even wider soundstage, depends on type of diffusion. But you can get incredible envelopment with diffusion. If you use combo panels one can have the best of both worlds. The reality is with wider dispersion speakers you can tailor the sound to your liking by using various types of acoustic treatment or not.
per toole, if the loudspeaker has poor off-axis response then the sidewall reflection should be attenuated/absorbed.
if the loudspeaker has good off-axis response, then it is up to the user's tastes or subjective preferences. although if for objective accuracy, the high-gain early-reflections that are destructive to intelligibility, accuracy, and localization will need to be attenuated.
however your statement about losing envelopment is misguided. far too many ignore the later-arriving sound-field when modifying small room acoustics of a 2ch stereo reproduction room. if the early reflections are attenuated, then that extends the ISD-gap which will provide a psycho-acoustically larger size of the room (since it will take longer time before any significant indirect energy impedes the listening position). the reproduction room will sound larger and allow one to hear more of the recording/tracking room ambience. attenuating the sidewall reflections is but one step, the other is to re-introduce lateral energy as a later-arriving sound-field to provide that passive envelopment. this is done by the introduction of 1-dimensional phase grating diffusers on the rear/rear-side wall, of which spatially disperse specular energy in a diffuse and exponentially-decaying manner for envelopment and spaciousness.
so when someone insists that attenuating first-order reflections removes spaciousness or envelopment, it is solely because the later-arriving sound-field is not addressed/managed. this is a case of operator erorr. the entire time-domain response should be viewed as a system of individual components. removing first-order lateral energy will assist with maintaining accuracy of the direct signal and increasing perceived size of the reproduction room (increasing imaging and localization), but significant energy must be reintroduced at a later time and from the lateral direction to provide that envelopment from the rear/rear-side wall directions.
for other subjective tastes, diffusion at sidewalls can be useful if they attenuation the reflections such that they are not keyed on by the ear-brain for localization, imaging, etc. gain, direction, time-delay, etc all are relevant.
