If you look at Soviet (okay, Russian these days) exercises simulating a strike on a carrier, it is clear that this is no easy mission. They are willing to put a tremendous amount of resources into a strike, and it’s clearly a one-way mission either for most of the strike force or for all of it. It’s also clear that they think it’s worth trying because of the danger posed by a carrier, or they wouldn’t keep trying to figure it out.
Having been on carriers (after I left the Navy) and on subs (never as a carrier escort but I have played against a carrier), I know that taking down a carrier would be extremely difficult. A single attack could easily cost Russia almost as much as the carrier cost us, and their probability of success (defined as a mission kill against the carrier itself, not just a few aircraft splashed or a couple of DDGs taken out) would still not be good.