Just going by personal experience, my omnidirectional speakers sounded best when there was no room treatment. They were calibrated to have a flat frequency response in the untreated room and they have been calibrated to have a flat frequency response in the treated room.
My speakers were designed to reproduce the sound of live music playing in a room, as if the instruments and musicians were actually in the room. They aren't designed to reproduce the space of the room. Real live, unamplified music doesn't require special acoustic treatment to sound good in a room. A real piano or a real guitar sounds best when played in a regular room where sound can bounce around and bring the music to life.
I'm not sure about what you say about unamplified live music being played in untreated rooms applies all the time or even most of the time. Often venues are treated in some way and some sort of DSP/EQ may be used. If you listen to any recordings they will have been processed via a mic or mics (micing recordings seems to be an art in itself) and using some sort of DSP or other recording techniques. The producer/engineer will no doubt have some target audience.
In any case playing live music and playing recordings of live music is not the same thing for two reasons:
1. Our listening rooms are usually smaller, sometimes much smaller. Small room acoustics are different.
2. A live recording if done well will capture the music plus the room it's played in - for example a cathedral. When replaying this in a small room not only do you get the recording from the direct sound from the speakers but also any reflections developed in your room, such as side wall reflections.
For these reasons I'm convinced some sort of room treatment is needed to extract the best from the recordings after they leave your speaker (whatever your speaker type) and enter the room on the way to your ears. Sure the brain can do a lot of work to filter out stuff but if it doesn't have to do that work I feel we can get more into the music in a relaxed and enjoyable way.
All this is described in Floyd Toole's opus, 'Sound Reproduction' as part of the 'Circle of Confusion' that we listeners have to wade through.
However, your personal experience trumps all and if you enjoy what you hear in your circumstances, that is the main point of the exercise.