In terms of optimisation analyses, to what extent has AD&D (2nd Edition)'s Charisma stat been analysed? How is it appropriate to proceed in an optimisation analysis of Charisma?
In terms of RPG history, the Charisma stat in 2e appears to be a bridge between rules that enable simulationist dungeon-crawling, and rules that enable character expression. 2e began with Charisma acting as a "pre-adventure" multiplier of action, in particular through expanding the party with NPCs. It also governs the reaction of non-Party NPCs and Party NPCs to encounters prior to the commencement of combat.
The 2e Charisma rules encourage henchmen and hireling spam, effectively enabling an "any-class" controller (with the Paladin being a specialist at this domain due to stat-requirements). The 2e Charisma rules also encourage non-combat encounter resolution through bargaining prior to combat, and imply the possibility of partial combat resolutions through parley, quarter, surrender and retreat (at full XP earnt IIRC).
A provisional analysis, to my mind, would indicate that making Charisma the centre-piece stat would allow for cheaper XP per unit of effort, possibly at the cost of treasure (and the remainder of the party being irritated at the controller). It would also change game dynamics from the "heroic four" to managing a pack of underlings. In general, it poses an optimisation problem as these "2e controller" powers resolve outside of the standard resolution systems for 2e (proficiency rolls, combat).
(Some interesting features here could be due to the system being insufficiently internally analysed, leaving exploits; or, this could be indicative of general "multiple resolution system" problem in optimisation).