I think being a Catholic with no connection to living leaders makes more sense than being an EA who doesn’t have a leader they trust and respect, because Catholicism has a longer tradition
As an additional comment, few organizations have splintered more publicly than Catholicism; it seems sort of surreal to me to not check whether or not you ended up on the right side of the splintering. [This is probably more about theological questions than it is about leadership, but as you say, the leadership is relevant!]
Consider the reaction my comment from three months ago got.