The Merlin has no really bigger footprint than the Sea King. In fact its main rotor diameter is one foot less, and while the fuselage is two-and-a-half meters longer, I believe it was designed to pretty much fit in the same space with the tail folded up; not least because it replaced the Sea Lynx on the Type 23 frigates. So it could just as well operate from an Invincible-sized platform. Of course the QEs will carry 14 vs. ten, but then there will be just two of them vs. three; and that's not a capability leap I'd consider worth the cost of doubling the total tonnage in class, with the associated cost. It's really more a case of you work with what you got and paid for. Of course you still got the extra capabilities for other mission types.
Very true, but its still a hell of a big helicopter to fit on a Type 23, and I gather getting the hangar the right size to fit them was part of the delay for the first of the vessels. Ive yet to check whether we intend to fit them on the Type 26 and Type 31 when they enter service.
In the end, its the choice made 20 years ago we are working with. For our purposes, Id suggest 3 carriers in the invincible class would probably do us just as well. OTOH, its hard to argue with the amount of stores or the deckspace 60000 tons is going to give us, particularly the Commando capability.
Rather than looking at it as just a small enhancement to ASW or more fighters, really there are several advantages here.