You are mixing two separate things. If the bulk of Bitcoin owners were to try to sell all at once, most wouldn't have anyone to sell to, and the price would go

You are mixing two separate things. If the bulk of Bitcoin owners were to try to sell all at once, most wouldn't have anyone to sell to, and the price would go way down. This has nothing to do with exchanges (although at increased load probably most of them would experience outages). The second question is whether most exchanges would be capable to transfer out all bitcoins they are currently storing for customers (a "bank run"). As far as I know, exchanges aren't supposed to be running a fractional reserve system, so they theoretically shouldn't have a problem with this, given some time to get data out of cold storage. Indeed, like banks a while ago, if they did manage to lose (or spend/steal) a part of the amount they are storing, they would simply go bankrupt at this point.