> messes with the valuation by inflating the supply

If a casino allows you to make play as long as you want, i.e. unlimited bets, does that de-value the bet?

If the shorted stock doesn't go down, people need to pony up the difference to buy it back; it is that capital risk that represents the "skin in the game", and why shorts aren't really unlimited, any less than an insurance company is limited in how much insurance it sells, by the capitol it holds to pay out on claims.