Earlier quoted context omitted.
What you are suggesting is a one-sided market where prices can only go up and there is no restoring force. That's dumb. What's worth knowing is that immoral conspiracies among short sellers are incredibly rare. I challenge you to find a documented case. By contrast, there have been many, many pump-and-dump sell-side scams, and without the short side there would be many more.
One sided? You buy, and you sell. The price goes down if there are more sellers than buyers. This is how it worked until the “professionals” invented all of this ridiculous nonsense so they could gamble on the markets. Buy or sell. And nothing more.
I do believe banning certain instruments from the market can have a positive effect, but I'm not sure if short-sell is one of them.