I almost never use HC. I find it clumsy and more often than not its lack of auto-fire nets me a lot of casualties. Area saturation with AC-HE or AC-I rounds, though, is a very nice complement to my squad, especially when coupled with the fact that direct hits are not necessary to do damage.
At least during the early tactical battles, AC-HE wielding troops can prevent a great deal of situations from going sour.
Say, for example, I have a unit 6 tiles away from a Sectoid, and that unit can either make one snap shot with a low but very much possible chance of missing, or retreat to a safe distance and allow the AC-HE soldier to eliminate the Sectoid without risk.
In that case, I would have spared myself a potential casualty by employing the Auto-Cannon's fire support.