a) people will trade 'virtual' shorts by betting in other markets on the share prices.
b) once you have people betting on shadow markets on share prices, there will be arbitrage between the real and shadow markets with hilarious results.
The idea of banning shorting seems very weird to me. Back in prehistory when my Dad worked in t'city (as a clerk) you had until settlement day to buy the shares you were selling (every other Tuesday) i.e. shorting. The Stock Market without shorting is like [where is the 'insert simile' command in emacs?]