Social media is a communication tool. What you’re seeing is evidence that normal human beings share interests and discuss them. That is not automatic evidence that the interest needs to be technologically exploited at the source. That this is not immediately clear is a significant driver behind the most reprehensible parts of the computing industry. I also think you’re overlooking that “I solved it in four! Yay!” is a mild extension of the anecdotes you’re hearing about five minutes and forget (they’re not mutually exclusive). I bet even the engineers who spent the last couple weekends solving for the optimal word are ready to put that bag down, too, and are probably just as strongly in that five minute group.
It already has a Share button that is implemented in the most respectful way possible for a user. Wordle’s backlog is precisely zero items long. Anything you’d do to it to consider social media would make it fundamentally worse. That you think it’s a social network in waiting leaves a metallic taste in my mouth and a bunch of despair for where we are.