eliminate shorting completely and let the economic side take place in where it belongs in a derivatives market place.
Well that's essentially what we have now in any stock that has a traded option, because option market makers are exempt from the naked shorting rules.
The trouble with your suggestion (assuming a prohibition on anyone including the MM naked shorting) is that it breaks the link between the derivative and the underlying because you can't arbitrage between them any time the imputed "derivative price" is lower than the stock price.
In the current version, if you short via an option, the market maker delta hedges by shorting the underlying. Hence the linkage is maintained. In your version, you wouldn't even get put-call parity, so your whole derivatives market would be out of whack.
But other than that, I like the concept. :)
Peter