I think the "different philosophies" point breeds all the others you mentioned. At our dojo, it's the exact same: I have a particular spin on things and our other instructor (MikeE) has a different spin. Our technique is certainly different, but not by much. And like you said, the students benefit tremendously.
What is different is how we choose technique. One person may choose a flowing motion whereas another may use a more direct irimi or other jitsu like that.
I think you hit it on the head with different viewpoints; everyone has a different angle on aikido, and some break off to form their own 'style' based on that angle. Shioda, Tohei, Tohei senseis and countless others have done just that.