This is basically what most professional navies worked out long ago and is the reason for the various USN CVS and SCS concepts, the RNs Escort Cruisers, Tiger Conversions, CVL conversions, Through Deck Cruisers (which evolved into the Invincible class), Italy's helicopter cruisers, then carriers and Japans DDHs.
There is actually a very good paper on Japans thinking on the matter, outlining how they originally wanted four CVS (one per hunter killer group) with Trackers and helicopters but settled on eight DDHs (two per hunter killer group) but only ever got four due to political and cost reasons. The reason behind their current through deck DDHs is to get helicopter numbers up to what is needed to contain and kill an SSN, this not just total number of helos but the number of spots to surge extra aircraft when a contact is made.
The UK has long worked on the principle that a helicopter on station can replace a frigate in the escort screen and hence why the Invincible class exist (original plans were for six of them). The more helicopters you have the better you can maintain a screen and the more effectively you can respond to a contact. If you establish the number of helos you need, including to cycle them through maintenance, as well as the number of spots you need to surge aircraft on contact. This is where a larger platform with more helicopters and more spots becomes economic as a single hull with multiple spots able to adequately support multiple helicopters becomes cheaper than buying and crewing additional escorts over and above what is required for task groups and other missions.
When you have a platform with five, six or seven spots you find it is large enough to have extensive maintenance facilities, magazines, fuel bunkers, command and control facilities, extra accommodation for specialist personnel, a hospital, even STOVL and other types covering off a wide spectrum of roles that may not otherwise be addressed. This potential and flexibility can actually be a minus as instead of concentrating on the fact that it is the most effective (including in terms of cost) way to get extra helicopters (and as importantly spots) to sea, many through ignorance or even deliberate/malicious misdirection ignore the key factor of the efficiency of the platform in enabling the require capability, i.e. X no. of ASW helos and helo spots and make it about escort numbers, alleged vulnerability, manning, STOVL fighters are more limited than CTOL ones, a CTOL carrier would be better (but unaffordable), need more than one CVH, will unbalance the force, etc. etc. The irony to provide the required number of ASW helicopters in any other way is actually more expensive, requires more manpower and will never be realised, meaning the fleet is actually less capable, less flexible and more vulnerable.
