"We can’t help but desperately compete in this unwinnable game of having the best collection of attributes to show off." I don't get it, because friends don't need each other to be the best person in the world at any given thing. Having things in common seems to be enough, no? Does anyone need to be "unique", a special snowflake in the world? In some sense friends are interchangeable, in that it's a total accident of circumstances which few of the billions of people on Earth you happen to hang out with. But I'm not clear on why "global uniqueness" is necessary for friendship. That seems to be an impossible standard, and it's not the basis of any friendship I've ever had.
"In my early attempts to make friends, I tried inviting people with shared interests to activities like sailing or grabbing brunch". I think the missing ingredient here is simply time. It's hard to become friends in just a few hours.
[Edit:] "One way to create a shared context is through shared struggle. This is why many organizations implement ritualized hazing to initiate new members, but the important thing is not the hazing, it’s the sense that you are working together with your fellow humans to achieve a super-human goal."
The super-human goal of getting your butt paddled by a frat boy? No, hazing is just a perverse power play, nothing more. They do hazing because they can, and get a kick out of it.