Exactly, or, to put it another way: right now synchronization is yet another way to share files either with someone else or with yourself, and there's already hundreds of methods for doing that, and once everyone starts using web applications exclusively, it'll be a non issue.

Web applications will not solve our synchronization problems

Example: You want to send a mail using Yahoo Mail where you attach a document created with Google docs. When you created that document you wanted to use an image from Flickr. That's 3 different services that needs to be synchronized. What happens when you add other web applications.

When/if people move to web applications, the synchronization problem moves with them.

I think you're talking about integration not synchronization.