Storing your media locally is fine, but you only have it when you're physically at your machine. To go portable you have to manage syncing files to an external device. Now you've got two libraries to manage.
Yes, we lived with this kind of thing since digital music existed, but it was a pain then and it's a pain now. Keeping one centralized library that any device can play from means less effort required to maintain the library.
Plus I can play my music in the car from my phone and never have to hear an annoying radio ad again.