IMO, we can only make all inter-arbitrator messages public if we make all that we do have to do with public information. In other words, remove the other functions; we would only handle cases presented on-Wiki, with no private information permitted.
We cannot legitimately turn the current arbcom system into a wholly public and transparent one without radically changing the scope of what we do, IMO.
I suspect that if the arbcom became a wholly transparent and public body/process, we would soon find the need to have a confidential body as well, unless we made a radical decision to have ALL processes on Wikipedia public.
I know that there are some who'd advocate such radical openness. No secret arbcom deliberations. No OTRS. No privacy policy? It would seem to follow. Checkuser data open to all to view?
It really depends on how important you see openness as being to the process.
IMO, I think openness is a useful but secondary value; historically, we've considered that principles such as "Wikipedia is an encyclopedia" and "Wikipedia is not an experiment in online democracy" as suggesting that if the interests of the end product are best served by having some private processes, we have them.
Of course, this post is a somewhat extremist view; of course, it would be possible to open arbcom proceedings up a little without going to those extremes. However, anything short of forbidding any kind of closed deliberation or discussion among the arbcom members cannot even hope to satisfy those who frankly don't trust authority and structure; and even then, I suspect, the paranoid would suspect clandestine communication.
-Matt