I've had a long-lasting opinion for banning elbows on the ground, not on the feet.
1. While it's rare any cut - come it from an elbow or a knee - stops a fight, it hinders vision, which surely has some effect. The one receiving the cut generally fights more aggressively to avoid a doctor stoppage, possibly with hindered vision. This takes away from the competition. He isn't necessarily down on points, he isn't hurt, but he has a reason to worry about other things than fighting.
2. Knees on the ground do more damage and cause less cuts (and if they cause a cut, it's from damage). An elbows sharp angle with not much space to throw with force is what makes them worse than knees, which can be thrown with more power (Pride - Randleman, Rampage, Hendo). Pro knees, anti elbows.
3. Elbows can be used to open up cuts (or open them up more) by rubbing them in the cut, whether that's a partially healed one or a recent open one.
4. There's a higher chance to score a sub from the back when elbows are banned. Punching requires more space than elbowing and makes wrist control easier regardless if the punch is a short hammerfist or a postured up shot. With the takedown-heavy judging, the guy on the bottom has a more likely chance to show his game. More finishes.
5. Less blood is more TV-friendly. Now bleeding from a beating on the feet or on the ground is fine, that's fighting. Unnecessary cuts affect the action and don't show damage, just give the assumption of someone being hurt. I'm no fan of watching a bloodbath, nor are many other people. And those elbow cuts tend to be artificial "damage".