If short barrels are really better/more accurate, then why do most competitors use much longer ones...?
Simple answer, because we suffer from barrel envy.
More complete answer is because people who want to excel in certain competitions will use equipment geared for that competition.
Short, stout barrels can be incredibly accurate and I believe those are the types of barrels favored by the benchrest crowd shooting at 100 to 300 yards or some such. I know very little about BR comps, so excuse my ignorance.
The tacticool guys and gals want to run around lugging their equipment from position to position and so long barrels can be detrimental to easy maneuvering. I don't know, I'm too old to play those games, but that's what I hear.
The OP said that short barrels are loud, I totally agree. They have more recoil because the rifle is lighter. They generate less velocity because they waste a lot of the wonderful hot gases making a bigger report instead of pushing the bullet faster.
My F-TR rifle wears a 34 inch barrel. I don't run around with it, as long as I can drag it from the back of my CUV to the rifle rack to the line and it makes weight, that's good enough for me. What I do want from my barrel is the most velocity I can get out of it, and still be able to reuse my brass several times. As has been stated several time, higher velocities mean less time in the conditions and in F-TR, at 1000 yards, that's a good thing. And we don't shoot for groups and we don't shoot as fast as we can pull the trigger, and we don't shoot just 5 or 3 shot strings.
Bottom line, get the barrel that fits your game.