Some airlines just give call priority, others give dedicated agents, and there can be a tradeoff. If dedicated agents are overwhelmed sometimes you just want to get through to someone. During actual high call volume periods an airline might roll over its elite members on hold to the top of the general reservations queue.
Such dynamic call handling makes sense. At American Airlines, though, Platinum Pro members’ calls get priority but will now roll over into general reservations instead of to dedicated elite agents for international bookings according to an internal airline memo.