...why should I care...
I'm not sure that you should ... but:
All of us should care what golf *is* and what golf is *perceived* to be -- just on general principles, and because if golf's image suffers, so will the game, sooner or later.
Every one of us will have a different definition of "suffers." Every one of us will have a different idea of the image we want.
The image I want for golf is: outdoors; exercise; camaraderie; competition; challenge; fun; welcome to all.
I think the golf cart diminishes that image. It takes away most of the exercise; it can undermine the camaraderie; it makes the round more expensive. But I understand that it's essential to the health of large swaths of U.S. golf courses, and near-essential to play many golf courses that wouldn't otherwise exist -- so I accept it, even as I rarely use it.
To my eyes, the golf board looks, as you say, goofy -- as goofy as, say, Doug Sanders' clothes. I think that those pastel nightmares, which many golfers emulated, made it easy for non-golfers to mock golfers. The golf board, I think, will do the same.
Call me stodgy; I am.
But, of course, to each, his (or, of course, her) own -- including his or her own views.