Well, maybe no competition when we're talking about institutional access rights on dry land. However, for everyone else, there's quite a bit of competition out there in the high seas.
But they could adopt an official policy of all publications being CC licensed and uploaded to at least one of a few officially sanctioned preprint services. That would do a lot to undercut the publishers going forward.
At this point a lot becomes open access after a few years anyway. The issue is historic papers but all of those can be reliably found on the high seas.