Isn't a bank run only an issue if the bank is using a fractional reserve? Cryptocurrency exchanges aren't banks; they're not supposed to keep a fractional reserve. If everyone suddenly demands all their coins at once, the exchange should have no trouble complying with that.

The only problem is that there's no way to know for sure whether an exchange is running on a fractional reserve or not.

Huh? This is pretty much exactly like Mt. Gox. At first Mt. Gox only suspended people's ability to withdraw USD, like Bitfinex. Then they suspended people's ability to withdraw BTC (apparently people have been experiencing delays getting crypto withdrawals to go through on BFX recently?). Even then they still allowed people to send money between accounts within the exchange, which resulted in a secondary market of people buying "Goxbux" from other people with money stuck in the exchange (at a discount, of course; basically betting that Mt. Gox was actually solvent).