Short selling allows for more efficient price discovery, market transparency and liquidity. Volatility is reduced but increases on covering rallies just as it does on selloffs (opposite sides of the same coin we call a free market).
Large institutional investors, investment banks and mutual & hedge funds would reduce their trading volumes if they couldn't hedge their trades, thereby reducing market liquidity. Besides, previous bans on short selling have not reduced market selloffs. In fact they often escalate the selling (as we've seen over and over again since short selling bans were introduced around the world from 2008).
Buying a risk asset like stocks using a margin loan or high leverage is the real risk to both investors and the market. This issue needs addressing, not free market trading. When markets become volatile, margin calls can cause more severe cascading selling than short sellers.
"In a bear market, bullish investors always come to believe that short sellers are 'driving the market down,' when in fact, the decline is almost entirely due to selling from within their own over-invested ranks.
Sometimes authorities outlaw short selling. In doing so, they remove the one class of investors that must buy. Every short sale (except when stocks go to zero) must be covered, i.e. the stock or derivative contract must be purchased to close the trade.
A ban on short selling creates a market with no latent buying power at all, making it even less liquid than it was. Then it can decline day after day, unhindered by the buying of nervous shorts. Like all other bans on free exchange, a ban on short selling hurts those whom it is designed to help." Robert Prechter.