It's begun- Shorters beginning to close their PNV positions, page-10

You are using the word 'efficiency', however, it could be replaced with the word you used earlier in the post - 'volume', as 'efficiency' is suggesting a positive outcome, and understandable, as that is your position.

As others have suggested, there are good arguments for keeping the shorting of shares of a company independent of other markets and wanting to sell without owning any shares could be limited to those other markets ( CFDs etc). With the massive increase in people and businesses day trading over the last 20 years, liquidity has already greatly increased (how different it is now from when I called up my broker on the home phone all those years ago!).

I think the share market would operate well by removing the shorts from the listed company indexes and moving it to external markets to do whatever they need to do there. After all, they are just taking a bet in reality. The financial people working in futures/options and banging out straddle strategies etc will disagree with all that, but we can see the manipulation that is occuring - I don't see that as 'efficient'.