I believe that giving CheckUser access to all admins would now qualify adminship as a "big deal." I'm not sure if I would even want that responsibility: misuse of the feature would be very easy to many.
And what would we do if abuse did happen, such as the public posting of certain users' IP addresses? I don't think that a ArbCom decision could properly punish such an individual. There are much many "real world" consequences to the revelation of this type of information. De-sysopping just wouldn't cut it, and neither would a year ban.
Yes, there would be some additional benefits to giving a greater access to the CheckUser privileges. But I don't think the costs outweigh the benefits, at least not right now.
-- Ben Emmel Wikipedia - User:Bratsche bratsche1@gmail.com "A fool sees not the same tree that a wise man sees." -- William Blake