Maybe this carts / no carts / walking argument also involves elements of another age old argument....is golf a sport?
I would challenge that if you consider golf to be primarily a sport or athletic endeavor, then maybe you also think that motorized carts should not be allowed, as part of the athletic endeavor of golf is the challenge and possibility of fatigue from walking, especially in the extreme heat or elements. Riding a cart for 18 certainly takes away at least a small part of the athletic challenge from the game.
If you consider golf to be more of a social pursuit, or that golf is a pasttime/ easy day social, then probably you aren't as bothered by motorized carts. You see carts as aiding in the enjoyment of the pursuit of golf, socializing and part of a day at ease. Golf is less about the athletics and more about the social or nature aspects for you.
I am not sure that either above view of golf is 'incorrect', and either view is only a part of the total thoughts each of us have on this question.
Few people dispute the need for carts for those physically unable to walk a course due to age or physical disability. Some common sense on the subject, along with looking at the course lengths between hole, the heat or weather conditions at the course (you couldn't play too much golf in Arizona's 110 degree heat in the summer without carts, could you?), and the traditions surrounding the course are probably in order.
I don't mind carts too much, as long as pace of play is not affected. I choose to walk almost exclusively, due to a number of factors including exercise, the enjoyment of a course / nature, and the tradition of walking. My reasons, my choice. Others take carts for their reason, as long as it is played within the course's rules, well, I guess we can't complain as much as lobby to get the course to change their rules.