I would argue that even people deciding to attack the higher rated player is part of it and is included in your edge.
But I can see how that might make it so that your goal of having fun is compromised in a given individual game when your rating is very high.
I think what you're really saying is that there is no way in free-for-all 4 player chess to be in complete control. I guess you want to be in complete control, and you conclude correctly that will never be the case in this game.
This game is more similar to poker in the sense that skill gives you an edge. This edge gives you no guarantees in any individual game but it does in the long term.
Unlike poker though there is no randomness, the variance is just based on the unpredictability of each player's strategy, and part of that still involves skill in adapting your game based on who you're playing against. But yes, it's still out of your control on every individual game.