So,why do france,UK, Italy and even Brasil have them?
Here, broadly we are talking about developing true BLUE WATER capability for Turkish Navy.
In light of that, a fleet of SSN should be the first priority. (I am not suggesting to abondan the idea of CSG altogether, rather just saying, considering the strategic logic for Turkey it should the second priority if possible)
Let me explain why.
A fleet of SSN has certain advantages over 1 or 2 aircraft carrier for medium powers like Turkey when it comes to developing true BLUE WATER capability.
1. First and foremost, when it comes to SUFFICIENT power projection with CGS only super power like USA (And maybe China) can afford that. Not even UK or France can do that even though they have carrier strike group with blue water capability.
because, France or UKs stand alone CSG capability is not good enough to fight an over sea war against a CAPABLE enemy. (Sure, they can bully some small and poor countries with that and win wars against them) But practically speaking, their CSGs capability is only deployed efficiently when integrated with other Nato assets, Most notably USN.
Why I am saying that? well, let's take an example.
(Hypothetically) If tomorrow a war between Greece and Turkey breaks out and France send a its one and only carrier strike group to support Greece, it is never going to be enough and Turkish Navy and Air force can overwhelm it and eventually sink it even though Turkey doesn't have its own Aircraft carrier.
If it were to be a US carrier strike group, it would be very different scenario, as US has lots of other naval, land and areal assets in the region to support that carrier strike group. And that is more or less true when US CGS is deployed anywhere in the world (In the Pacific, Mediterranean or Persian gulf)
The same problem Turkey could run into with its own stand alone carrier strike group trying to fight an oversea battle far away against a CAPABLE enemy completely on its own.
2. In that case, A fleet a SSN can effectively fight a war anywhere in the world completely on its own and has relatively better chance to win it. (In its own operational domain obviously)
3. Also when it comes to fighting numerically and conventionally superior enemy, SSN has the upper hand compared to carrier strike gouprs.
Lets say for example, if 1 CSG goes against 2/3 enemy CSGs it has less chance than 4/6 SSN going after two enemy CSG to sink them. (To understand the effectiveness and capability of SSN against carrier strike groups compared to conventional suface combatants, we need to dive deep into how modern naval warfare is fought)
Let's just say for shake of simplicity, modern SSNs are equivalent to stealth fighter in its capability and effectiveness when compared to other naval combatants.
Having said that we also have to keep in mind that, only USA, UK and Fracne has true BLUE water navies.
Even India and China despite having multiple aircraft carriers each, are still not consider true BLUE water navies yet.
Because, along with the lack of logistical capability to sustain large scale overseas operational deployment of CSG like US or UK they also lack proper underwater escorts. (Current Chinese SSN are too noisy and India doesn't have any SSN yet although they are going to lease one from Russia) which is most essential part of CSG to Protect the mother ship.
Sure, it is possible to deploy carriers with conventional SSK escort like India or China do, but it limits the CSGs full potential and does not allow far away combat deployment.
In a nutshell, without proper SSN escort a carrier strike group does not reach its long range blue water capability. ( And this is precisely the point for turkey to have a heavy carrier, otherwise thank it’s advantageous geographical location most of the surrounding regions are well within range Of TurAF)
That is why despite having carriers expect US, French and Royal navies, others are still not considered TRULY blue water.
More or less similar reason why Brazil is now primarily focused on building its FLEET of 4 SSN (with ToT from France) and a new carrier is their second concern.
Or the reason why Australia is going to spend over $300 bullion on its SSN program rather than building big aircraft carrier (and relatively cheap conventional submarines)