You can enable and disable pretty much everything – except Files. That’s because it’s the core app and others like Gallery, PDF viewing, Music etc of course rely on there being files. There have been requests to even make it possible to disable the Files app, but we don’t really see that as priority and rather focus on keeping ownCloud rock stable and secure while still driving features forward. We are a very small team and an open source project, so I guess that’s understandable. :)
As a really dirty hack, meanwhile you could just hide the Files icon from the menu via CSS. But, well … ;)