If traders lose confidence in Tether, won't they sell Tether to buy other cryptocurrencies, thereby driving the price of Tether down and the price of other cryptocurrencies up?
Initially yes, but I think we would also see a flight from cryptos in general shortly afterwards because of the risks posed to the whole space by a collapsing/fraudulent Tether.
Why would exchanges collapse if Tether goes to zero? They wouldn't collapse if Ripple or Iota went to zero.
To an exchange, Tether is just another cryptocurrency. Traders deposit Tether, other traders deposit Ripple or Iota, then the traders trade and the exchange takes a cut.
If any of these goes to zero traders might get wiped out, but how exactly does the exchange go bankrupt?