Almost every business I deal with has a good case for using attachments. It doesn't matter if they aren't the most efficient or most secure way of transferring files, the functionality is there and if the person is sending an email anyway it is the most convenient way.
As an example, when we send out quotes we generally send them as an email with attached PDF. The email body contains a covering description and the PDF contains the quote itself.
To even consider a system whereby we have some hosted service and say generate a unique URL for each hosted quotation really adds nothing for us or our customers (well apart from being able to look at a log and see when they downloaded the quote, which is pretty useless information)
Other times we may be collaborating on a document with a client (perhaps it's a spec that requires amendments either end) The easiest way of doing this is to mall the document backward and forward with amendments attached. Yes we could have some fancy version control system but most of our clients would be put off by the complexity. So now by offering URL's we have to support upload as well...hmmm
Now in some cases I agree. If I want to share my holiday photos, mailing them to 20 friends is a silly way of doing it. In a case like this hosting them and sending everyone a link would make much more sense.
It's a case of right tool for the right job, If I want to collaborate on a document or send a small file within the context of an email then I want to use email to do it. If I want to share a number of files with a number of people then there are better ways.