These events ultimately lead to the creation of the Federal Reserve for banks to participate in a semi-cooperative system that didn't devolve into save-yourself during times of crises.
The story here is that "unless there is a massive run" is actually a fairly common event.
I'm not saying that Tether the company is not shady. They should definitely be more transparent about what assets they are holding and their collateralization, but I think the risks of total collapse are largely overblown.
As an exchange, if you keep some reserves in USDT and you think it might collapse soon, you might have an interest in dumping your positions before it completely loses value. Maybe exchanges would benefit from responding to such a situation collectively as you suggest, but I think it's likelier that they will just protect their own interests as individual entities.
At some point, total collapse of Tether’s pseudo-dollar will happen when the revenue generating exchanges feel they are support bad-money with good. All it takes is one player signaling a lack of support, and others stop supporting as well.
It’s a human psychological problem that’s a old as time. Think crypto can win over human rational to preserve self-interest? (side note: manipulation of self-interest is the goal of “weak hands” / “diamond hands”)