What a thoughtful question, thank you Dave! I think in this framework, shared struggle is a necessary condition of perfect friendship but not a sufficient one.
It all depends on how the two (or three or four) parties in the struggle behave. Do they cooperate with one another? Do they share real moments of vulnerability? Or is it more of a quid-pro-quo relationship? A trading of favors, if you will?
You can handle shared struggle with friendships of utility too. You can even use your friendships of pleasure to distract yourself as you figure out how to handle the struggle on your own. But if it’s a real, combined effort in which you and your friend show your true selves to one another, where you don’t fight the exposition and hope the other accepts you as you are, then, that’s the kind of shared struggle that can lead to a perfect friendship.
Hope that makes sense!