Why does short ratio use "average daily trading volume"?

My understanding is that once a share is borrowed, it can't be borrowed again (legally, anyway).

That has always been my belief but others here have stated that is not true. Given that the short interest in GameStop was around 140% then either there was 40% of illegal naked shorting or a share can be sold multiple times. I still don't know the factual answer but I'm now leaning toward multiple times.

So here's what happens in your hypothetical example:

The float of company XYZ is 100 shares.

+1 Bob owns a share

-1 Firm A borrows the physical share from Bob to short it and sells it to Nate

+1 Nate owns 1 physical share

+1 John owns 1 physical share and will become either a lender or a seller

The shorting by Firm A creates a synthetic share (+1 Bob and -1 Firm A) and Nate becomes the physical owner. So there are now 99+1 physical shares, one synthetic long share and one short share (+101 long and -1 short).

When Bob sells his share to Alice, Bob's broker requests the loaned share back from Firm A. Firm A's broker tries to borrow a replacement share either in house or from another broker. If a replacement share is found, John lends his physical share and he replaces Bob as the owner of the synthetic long share.

If a replacement share cannot be found, Firm A receives a forced buy-in notice and must buy the share back to close the short position, In this scenario, John sells his share to Firm A. The end result is that Nate and Alice each own one physical share each (replacing Bob and John) and the synthetic share and the short position no longer exist.

I hope this makes it clearer and I leave it to you to figure out short stats for the different scenarios.