It is not uncommon for authoritarian regimes to use a preposterous proportion of the population as spies, mostly recruiting them with threats, not pay. Stasi informers are an unusually well-documented example.
Threatening someone into providing copies of any keys they currently have seems a plausible attack under those circumstances (simply taking over a detained person’s phone is also common today). Sometimes you’d want new members to get all the group’s history, and sometimes you would not.
Could transient keys be used to do blind groups in which everyone can talk to others?