Your explanation makes a lot of sense. Nonetheless it's bit of a hard sell as it seems to parallel fractional reserve banking to a degree, and we've come to accept the later as the best currently available compromise.
You never look at the value of a dollar as the % of total dollars in circulation. The value of a dollar is rather defined by how many goods/services/other currencies you can get in exchange for it.
With stock it matters a lot more how many % of a company is represented by a single share.
Similar, each short seller not only adds a _virtual_ share to the market, but also has an obligation to later on buy a share back.
Again, to be super clear: for everyone but market makers, the law is you have to locate the borrowed share before selling short. Market makers can naked short to provide liquidity in a buying frenzy. Given they're shorting into a buying frenzy, they tend to be quite motivated to immediately cover themselves.
We have lots of people shorting GameStop. We have zero evidence anyone is improperly naked shorting.
I think naked shorting would be a perfectly valid thing to allow every investor to do, you clearing house would just want to ask for pretty high margin requirements.
Very similar to how there are covered call options, but also naked call options. And the economy hasn't collapsed either.