Bart,
I agree with you - the game is different and it is not just the walking/cart element.
The execution of the cart ball game is very similar to the execution of the parkland golf game. ie) target golf.
Links golf is more "fun" because all of the things you called out make it more of a "thoughtful challenge".
Most courses in the US are in their basic strategic form - Hit your drive here, hit your approach over here to the green, try to make a birdie. The game is about score.
Links golf is all about thinking about where to hit your drive - how high/low, left or right of your target because of the wind and the roll, then (if you are safe) your approach is all about - where is the pin, where do I land the ball to get it there, in front of the green?, on the green?, how high/low, which club, etc. etc. The game is much more of a tactical battle against the course and the elements - where score is almost irrelevant because depending on the day a par 4 can be playing like a 3/3.5/4/4.5/5 or even 5.5.
It is a very different game - and I think the fescue turf element is huge because you have to pick the ball off the ground, for the most part, and you cannot expect to land the ball on the green and have it stop dead or spin back ten feet because of the undulations and firmness of the ground.
I always find that my first several rounds at the "home parkland course" after a trip to play some links golf are disappointing and haphazard - something I like to call "links withdrawal" which is what you get from several days, or even a round, of "links heroin"
Links golf is the highest form of the game - there is no doubt about that (IMO)
I love playing or reading about courses in the US that incorporate the elements of real links golf - and I hope that many many more are built in the future (where possible) as opposed to the target stuff that is so prevalent today.