While I appreciate fighting fire with fire, this seems like a lack of imagination to me. Countering the US' carrier superiority with submarine superiority seems like a more creative solution to the Soviet problem. Sea lane control, based on submarines, seems like it would give the initiative to the countering power. In your opinion, would this be a better path to follow, or no?
Subs, especially 1940s-1950s boats, are fairly limited in what they can and cannot do. Although the U-boats showed us how deadly subs could be in the right hands, I still think the pre-NATO Western bloc would have been able to call the shots at sea against a Russian sub-oriented fleet. Had war broken out, Soviet subs would have had to navigate a variety of defendable chokepoints to reach shipping in the Atlantic or the Med. Combine that with the UK's and US' ASW tech and experience base from WWII and things start looking even grimmer.
Coordinated wolfpacks and saturation attacks on on TFs might have yielded some results, but, to the best of my knowledge, these weren't tactics used by Russian sub skippers in WWII. Generally, it's good to be at the top of the learning curve when the shooting starts.
Plus, I'm not sure subs would have fitted in with the goals of the early-Cold War USSR. While the Soviets weren't the rabid expansionists some make them out to be, there's little question that they wanted a piece of the pie. And carriers fit into this vision quite well.
Carriers and their battlegroups/task forces are flexible, powerful means of force projection. They can engage targets on the water, over the water, or under the water and they can do this virtually anywhere in the world.
For a nation looking to plant and protect its interests abroad, carriers make quite a bit of sense. Plus, they flattops come with a prestige factor and potential for "showing the flag" that doesn't come with many (if any) submarines.
So, given the Soviet's goals (expand Communism, plant and support satellite states, grow as a recognized world power), it would have made a fair amount of sense for Stalin to have made building CVs a goal.
(In the same vein, it also may not be unreasonable to link China's recent efforts to build carriers and procure air arms with its growing role on the international stage. Obviously, there's many other factors behind their decision, but this might well be one of them)