To my mind, ITIL is, to some degree, enterprise architecture. I don’t see a reason [why], when you have six different service desks in an organization, you can’t have one process that they all follow and one database that they all put their incidents into.
My experience with ITIL is quite limited, but based on my understanding, it seems much more concerned with change management and ongoing processes as opposed to EA's focus on business driven, strategic, target state realization. EA is, with all due respect, is a bit more involved than 'recording incidents' in a common repository.
That said, I'm sure that both practices have their place, and many organizations could benefit from either or both.