The Rapier and Dagger were air cooled but Napier moved to liquid cooled for the Sabre, what was the reasoning for this?
Cost isn't a big factor in a fighter engine if it buys you (reliable) power.
In comparison to the contemporary V12s (Merlin, Griffon, DB601/5, DB603, Jumo 213) the smaller cylinder displacement of the Sabre meant it ran higher RPM with a consequent power increase.
I suspect the reason Rapier and Dagger didn't do better is that a 24-cylinder engine that delivers the same power you can have from a contemporary 12-cylinder engine probably is going to be more expensive than the engine with the lower parts count. I have no idea of actual historical prices, though.