It's an expensive choice because they're expensive ships to build, even without PAAMS.
The big development cost on Type 45 was PAAMS & its integration with the ship, not the hull & propulsion. C1 & C2 would require modification of a T45 hull, & integrating different systems. That means development cost. The development cost of doing that with a Type 45 hull might be less than designing new, but the difference is unlikely to be anywhere enough to make up for the higher cost of building T45s, rather than smaller & cheaper C1/C2s.
IIRC the plan is for C1 & C2 to be less than £500 million, especially C2. They'll be getting a lot of the same kit as the upgraded T23s, & stuff will be recycled from T22s & T23s (after refurbishment, no doubt) as they retire.
What do you mean, release the C2s?
I agree that some smaller, cheaper ships could do constabulary roles & spare the frigates, but most of the tasks envisaged for C3 are already being done by smaller, cheaper ships than frigates, & it now seems it's preferred to run them on. Building enough C3 to cover the West Indies station, then stopping for a decade or however long until more are needed for the other tasks, might not save anything.