The best way to understand what the Soviet (and then Russian) role for the Kuznetsov can be found by their own designation of its class.
It is not a fleet carrier, or a true carrier at all as we in the west view it. No, they called it a:
" tyazholiy avianesushchiy kreyser (TAKR or TAVKR) "
This stands for a "Heavy aircraft carrying cruiser."
It was never intended to "project power the way a US or western carrier like the CDG does. it was never meant to. Its roll was to support and defend strategic missile-carrying submarines, large missile carrying surface ships of the Soviet/Russian Navy, and to defend bastions where larger number f Soviet/Russian maritime missile-carrying aircraft could rendezvous far out to sea and then be dispatched on their missions.
A completely different mind set to how to use such a vessel.
The Chinese got one of these hulls on the cheap and refit it...but they have quickly established a strike aircraft (the J-15) which, although it looks like the Russian SU-33, it is quite a bit different in the various avionics, functions, and armament it can carry as a multi-role aircraft that and can perform either fleet defense or strike at sea missions, instead of the predominant role of the SU-33 which was Fleet Defense.
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