While it is true that stronger players are generally better at lasting longer, there are many cases where a player cannot ensure their own survival, no matter how well they play. One argument for having a low king value is that the king is a significant piece regardless of its point value. Being a skilled player implies that you are able to get as many points as possible over the course of a game, which correlates to some extent with lasting longer on the board. So I don't believe there is any reason to increase the king value.
Only the first king that get captured should be valued 3 points. The second should be valued 4 points, and finally the third 5 points. The reasoning is that the most skilled players "last" longer on the board.