I think this "is allowed" for the same reason that I can borrow a book from you, sell it on Amazon, and when you ask for your book back, buy a copy of that same book on Amazon and give it to you - but in the meantime, the person who bought your book from me can lend it to yet another person, who does the same as me.

In other words, this works simply because stocks can be sold and borrowed, and they don't carry provenance with them. To stop this, you'd have to do the equivalent of DRMing books and revoking the first sale doctrine. Which I imagine would turn shorting into a much more complex market mechanic than it is today.

(Disclaimer: the extent of my expertise on stock markets is me knowing how to spell "stonks".)