@asctim my Dad was a trumpet player and I've been conjecturing for years why no recording of a trumpet (and worse, string sections) doesn't sound anything like live.
My theories are:
1) Dispersion pattern, as you noted.
2) Mismatch between speaker type and mic type
3) Trumpet has a DC component to the outflowing air column that may create complex phase variances microphones can't capture or speakers can't play
It is a constant annoyance when guitars sound 8 feet wide, violin sections sound like a bad synthesizer, pianos sound like they are mounted vertically on the front wall, etc. and I agree recording technique is largely to blame.
I've considered building a pair of dodecahedron mics and matching speakers to see if that works. But 24 channel stereo just isn't something current media and gear can handle.