Although you may have a valid point , please don’t discard the fact that Sea harriers have a weapons payload of max 3600kg. And they performed extremely well as a light attack naval aircraft in various instances; one of which was in Falklands.Hürjet already has a low payload, less than half of an F-16 and most other fighters, it definitely needs a stronger engine to be a proper fighter. I genuinely don't see the point of turning such a weak jet into a carrier based fighter when its sorties will be very limited.
So don’t under estimate a Hurjet with a 3 ton payload.
Ideally the cheapest and most effective way for us would be to build a sister ship of TCG Anadolu, and buy 36 F35Bs as US is offering us to go back to the JSF program. These planes can have a weapons payload of 22000 lbs. (10000kg) - a fact that has been tested by RAF.