For a short term 10 day lock, just send bitcoins to a client on your own computer and back up the file.
There's not a ton of benefit for the exchange to do this since you have these other options at your disposal, but they would in turn take on a lot of customer support tickets for people who want to unlock wallets in panic days, etc.
that's true, but in a way it would also prevent those panic days from even existing. and i agree with the majority of the posts in this thread, except, it's not always practical to hold your bitcoins offline if they are invested on say, HavelockInvestments. yes, it could very well be hacked however that is beyond anyone's control at that point. unfortunately these hackers who probably work for the United States and Chinese government, are making Bitcoin's ventures extremely risky.