Isn't Netflix the poster child for this, and haven't they been for a very long time now? Not the content, which resides in their and others CDNs, but the back-end, webservers, databases and management systems are all supposed to be in the cloud now (after a long time migrating).
> I think it's a really hard thing to try and bolt on to a legacy system
There are different levels. Architecting a sharded database solution before you need to might be a bit excessive, but designing for multiple web, storage, or processing servers, etc from the start even if using bare metal is smart, and allows (relatively) easily adding capacity even if you are just colocating somewhere. At the point where you are already able to add capacity by scaling hardware, the cloud is a fairly attractive target, especially since automating the steps you take to add/remove hardware is likely trivial if you've already been doing it manually for a while, as the rough edges have likely been smoothed away somewhat already..