Actually you don't need to keep stablecoins on exchanges. Keep in mind that Tether is on the OMNI network which is basically the bitcoin blockchain and the ETH network which runs under the ERC20 network. So you can actually keep it in your wallet on your computer.
This is important because you can actually keep your stablecoins on cold storage. For ETH ERC20 stablecoins you can use a Trezor and for Bitcoin OMNI network Tether you can use the Armory cold storage option and you won't need to worry about them getting stolen like your crypto.
Another good thing about Tether is that you can lend it out on Bitfinex or Binanace and get like 10% interest per year. There is no bank that will ever give you an interest rate that high so its another pro of stablecoins.