That's a major lock-in mechanism. Data stays in for the compute. Which is a major pity for Microsoft since all the marketing measurement startups got built on top of AWS while Azure has superior analytics tools.
I mean, it doesn't necessarily solve anything if you're using it for public facing apps, but if you're doing a hybrid solution with Azure you can buy unmetered ExpressRoute ports and at least avoid the metered bandwidth costs back to a datacenter.
Also funny story, I was 14 or 15 and was trying to figure out a name for a stupid little chat client I was trying to make in C#, and somehow azure popped into my head. Not surprisingly azure.com was taken and just had a generic microsoft landing page (this was a little before it was announced in 2008).