Doing originals, you end up writing parts that use licks you know - swimming in your own little pool of confidence, where you know what you're doing. Learning parts that other people wrote will stretch you - force you out of your comfort zone. I have been in original bands, and you know your tunes, in the keys and arrangements that they were written in, and....that's it. It's fun, but if someone asks you to do something else, you can suddenly be a fish out of water.
I'm doing church gigs now, and although there is some repetition of songs from one church to the next, I am constantly learning new tunes, and the different arrangements and keys you end up playing stuff in really stretches you (we play in whatever key the singer feels most comfortable in). I'm now much more flexible in terms of that stuff - this weekend, we're doing 8 tunes, and 5 are in D Flat (aka C sharp). I've never been in a band where we wrote tunes in D flat.
i don't think that has anything to do with originals vs covers. you can always stretch yourself with originals especially if you look outside of your genre for inspiration. as far as different keys goes, we as a band make sure we use all sorts of keys to change things up. as an instrumental band we feel that is important to keep things sounding fresh.