The only benefit of an open door in an audio room is that it prevents some of the sound from reflecting off the door that used to be there.
No walls at all would be the optimum situation. That's not achievable in a domestic situation.
It is true that the sound will decay as it propagates into the room. That's because radiated sound whether from cone speakers or panel speakers expands in size as tit propagates into the room, thus losing intensity as it moves forward.
This is true for most frequencies. Below about 200 Hz, things change. Some sound waves are actually reinforced because a modal frequency (or its multiple) is excited. Resonant decays can last for several seconds whereas non-resonant frequencies last for less than 300 milliseconds or less. I have a resonance issue at 40, 80, 120 Hz. I have extensive traps, but taming these low frequencies is very challenging.
Acoustic traps are far more effective than any other kind of treatment for the normal listening environment. Opening a window or door here and there will alter the sound somewhat, but will not be nearly as effective or consistent as traps (fiberglass is the material of choice. Foam "egg crates" are useless.).