Everyone thinks a navy should use a navalized landplane fighter. Britain and Germany did. Well, Japan and the US didn't. Why would they? Their navies weren't bastard step-children. The Soviets didn't build their carrier and they didn't make their naval fighters.
While the British did use three navalized landplane fighters (Gladiator, Seafire, Hurricane), most of their aircraft were designed as carrier aircraft. The FAA top scoring fighter of all time, the Fulmar, was certainly not a gone-over landplane.
As for the Soviets, we don't know of course what path they'd take. Certainly with enough money and time anything is possible. If the Soviets follow the German or Italian model of aspiring to one or two carriers, then it would make sense to use land based aircraft. On the other hand, the USN model justifies a fleet of specialized carrier aircraft.
By 1944, the USN had 14 Essex class (each with 90+ aircraft), 9 Independence class (33 aircraft), 1 Yorktown class (90 aircraft), 1 Lexington class (78+ aircraft), 1 Ranger (78 aircraft), 50 Casablanca class (28 aircraft), 2 Commencement Bay class (34 aircraft), 4 Sangamon class (25+ aircraft), 1 Avenger class (15 aircraft), 1 Long Island class (21 aircraft). That's over 3,400 aircraft, plus those used in training and cycling through retirement and replacement, or nearly double the size of the entire operational Italian air force of Sept 1939.
If the Soviets plan to operate a naval aviation system requiring nearly 5,000 aircraft then I'd say they'd build something custom. But then again, they did build 230-odd Yakovlev Yak-38 solely for the navy, so who knows what they'd do?