I think you can explain it by the visible part being a hologram projected in order to make avoiding beams easier for friendly fighters.
"Avoid the beam and you won't get hit, pilot" would be much more difficult to execute (in fact nearly impsooible) if you couldn't see the beam.
That would also explain different colours of the beams, it's for distingushing enemy beams form friendly.
Also, beams cannot be projected on HUD, because EMP can screw it up and no one wants to fly into one just because of this.
Of course, that won't apply to fancy MVPs beams, but they're non-canon (though very cannon

) anyway.
As for space shotguns, they were mostly useless, not matter where I encouncerd them (except one place, where they were diverted from otherwise overpowered weapon, but you this mod is unreleased jet).