There seems to be one thing that no one is adressing. Tether can't be pegged to the USD and be backed 1-to-1 with USD. You have to choose.
If it's pegged to USD, Tethers are issues whenever Tether's price drops below $1 and Tethers are burned, destroyed or otherwise removed from circulation whenever the price goes above $1. However, if Tethers are backed 1:1 by USD, the price of Tether is irrelevant. It could easily go way above $1 if people are in a rush to get 'out' of crypto.
Seems the idea is supposed to be that it is "backed 1:1 by USD" (option 2) and that instead of changing supply portion of equation (as you mention in scenario one), arbitragers fix it by changing demand (increasing as it goes below $1 and decreasing as it goes above $1). Likely the floating supply changes as well depending on value (e.g: arbitragers buy below $1 reducing supply and hold, then sell above $1, increasing supply).
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4I think you have it the wrong way round. If a Tether goes above $1 (say $1.05), Tether Ltd can make 5 cent by issuing a Tether and selling it for $1.05. It owes $1, but owns $1.05. Conversely, if the price of a Tether goes below 1$ (say 0.95$), then Tether can make 5 cents by buying a a Tether for $0.95. It owns 0.95$ less, but owes 1$ less, making it a 5 cent profit. If Tether keep doing this, they could make a profit.
The problem as a I see it is that a) we have no proof of Tether's reserves (and the onus is on them to prove it, not us) b) I can't see the above mechanism working, because Tether can only really be bought or sold in BTC. c) I don't think Tether Ltd (if it even exists as an incorporated entity) even has access to dollar bank accounts.
A possibility is that Tethers are in fact backed by BTC.
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