There are A LOT of players who suffer from a severe lack of awareness about the fact that they have become group leader. Problem: they don't activate "looking for replacements". There are easy solutions to this:
a) Make it the default to look for replacements. I never had a situation where I didn't want them. Makes no sense to not do this.
b) Make the leader accept his leadership role actively (ie. confirm). If he doesn't, give it to someone else who does.
c) Allow everyone to start searching for replacements. And retain the current behavior for non-default group privacy.