The ability to sort through metadata to find your books as easily as in calibre itself is the main reason. Most ereaders/apps do not support a lot of metadata (series I'm looking at you), and certainly not calibre's custom columns.
Connecting wirelessly is another good one. Especially via the content server from half a continent away if necessary.
Also, if you have different formats, CC can handle all of them and simply tell the appropriate app to open PDF vs EPUB vs MOBI/AZW3 vs comics etc.