But if "folks desperately try and exchange their USDT for something they can sell at a fiat-backed exchange" then surely the most desperate will be willing to take a haircut on their Tether to get out of it first, and then the Tether price collapses anyway, through some combination of the exchanges shutting down trading, drawing down their own collateral to maintain the peg (and then running out), and/or the exchange reluctantly allowing the price to float?
Like, the too-big-to-failness is definitely part of why it's still a thing, but that just means that the real buyer of last resort is other large crypto holders who don't want the ecosystem to collapse. That's great for Tether-the-company, and maybe good for Tether the coin, but it seems to me sort of distantly related to Tether allowing direct withdrawals.
There's an obvious mechanism for maintaining the peg if Tether allows large holders to redeem Tether: those holders buy any slightly discounted Tether, then hand it back to Tether and redeem it and keep the tiny profit. This will work but it's just Tether propping up the price with its capital with extra steps...
Beyond that, you are correct of course!