Most shares are held by companies: either pension fund, to create your ETFs, mutual funds, or holding for you in normal broker account, or financial institutions, to provide liquidity, to put to work the pension fund huge inventory (most hedge fund short-selling is done with pension funds' dormant inventory using an investment bank middle-man), or by companies needing to store money somewhere other than cash.

I don't know many individual directly handling shares with the exchange and the settlement. How do you avoid the enormous volume of trading that happen due to retirement account reuse for shorting ? Would you forbid that too, removing the incentive for company to be honest because nobody can short anymore ?