With regards to room side-treatments to reduce lateral reflections,
I think it's fair to say studies have shown the majority of folks tend to prefer spaciousness and side reflections may aid that preference.
And past advice to universally avoid direct lateral reflections may well be misplaced.
But that advice still holds for a significant minority I think.
Personally, I don't care what the majority prefers.....
and don't like to see majority preferences becoming some form of accepted norm for how things work or how things are best done.
I'm also in the camp that thinks type of music preference has a lot to do with lateral reflections.
I don't care much for classical, nor for a reverberant sound. Give me studio pop, rock, blues, country, electronic, folk, hip-hop, dub, etc etc with tons of clarity and dynamics.
My favorite sound is a small live venue with good acoustics, where instruments are either unamplified, or if amplified, each has its own speaker stack.
Leaving the PA to handle vocals only. I love the sound of a backline, rather than a mic'd backline fed into the PA.
This is the sound I try to achieve in home, and squelching early reflections helps achieve it.
In fact, the best "at home" sound I've heard, comes from fully minimizing reflections ....setting up outdoors.
When conditions are right, with low outdoor noise and no wind...this is often preferable sonically to anything other than an excellent live performance.
So like i say, to heck with majority preferences in audio
We can all have what we want, eh?