As another commenter says, it helps the bullshit detector. Why know why anything works? If we just follow advice blindly, it may do us no good.
Your line of questioning is all wrong. You said, "I would posit that there is not a single person who read that blog post and thought 'gee, I should laugh more often because it has all these health benefits!'"
Therein lies the flaw in your thinking. You don't read something like this and think you should laugh more just for the sake of laughing and its health benefits. Instead, you'd read something like that, understand WHY laughter has those benefits, and then make an effort to put yourself in situations where you'd be more relaxed and open to laughter, like hanging out with funny friends or taking a date to a comedy club.
In fact, you answered your own question: Why do we need to know why laughter improves health? Is it because laughter helps cope with stress?
BOOM. You answered your question.
Maybe that's one of the reasons, but if you dig deeper, maybe there are more. Then once you begin to understand how and why certain behaviors and situations affect our lives, you can adjust accordingly. Maybe you don't need to laugh all the time if you understand that laughter is primarily a coping or stress-reduction mechanism. Maybe you can go do other activities that have the same effects.
You need to think about this stuff differently.