Aside from being all but unenforcable, Restricting short selling like that will almost certainly cause stocks to become overvalued. Short selling is an important balance on overvalued stocks, and there are cases like the Enron scandal where short sellers were the first to detect a company is engaging in fraudulent behavior[1]. Restricting short selling would allow companies cooking the books to keep their stock values at artificial levels despite investor skepticism
It may be in the national interest to impose "reserve requirements" on brokerages in order to prevent too much perversion of market prices.