I think it's reasonable for people to want to limit that. The trouble is that you would need to require brokers to prevent short selling stocks that have been already been borrowed and short sold. Aside from tracking a tree of stock ownership changes at the brokerage level, this would de facto create two similar but different assets for every equity: those which are "clean" (have never been sold short, or the short position is closed) wnd those which are "dirty" (have been sold short at some point and the position is not closed).

This is trickier than it might sound, because you are in some sense restricting the rights and capabilities of some subset of the shares. That has valuation implications.

I am not saying it can't be done or even that it's undesirable; just that the mechanics of this are nontrivial to enforce.