Historically, penitent clergy privilege arose because of the following:
1. Catholics in particular were/are taught that if they don’t confess their sins at the Sacrement of Confession, they risk hell. For example, when I was a kid, if my dad found out that I had not been to confession for a few months, he would treat it like a medical emergency; he would look up which church was holding confession on that day, and drive me there.
2. It occurred to some law enforcement people, or litigants, that one way to dig up dirt on an accused or opposing litigant, was to subpoena their parish priest, and cross-examine the priest about all the bad things that individual had done.
This is clearly unfair. So the penitent was protected at law. Spousal privilege, legal professional privilege, and privilege in aid of settlement are other types of privilege designed to stop such unfairness.
The main point to note is that the privilege evolved to protect the PENITENT. It did NOT originate to protect the priest (or Elder).
Of course, the law on penitent clergy privilege in various countries and states has been codified, and because of the words of the statute (particularly in some US states) may be broader than that. However, I think it is outrageous that Watchtower is trying to use a type of privilege originally devised to protect a penitent, to instead protect itself and its elders.