I dabbled with this idea. I got one of those Amazon 2 wheeled luggage carts. Mine didn't have a stool attached, but it looked identical otherwise, all the way down to the undersized wheels. It only took me one round to bail on it.
Problems:
Too short. I kept kicking it as I pulled it behind me.
Not hill friendly. It fell forward whenever it wasn't set at the correct angle on an incline.
Occasionally it bounced enough to tilt over, and I kept dragging it and picking it up.
It needed a wider wheelbase w/ taller wheels and a longer pull handle.
Even though I could've modified it for cheap, I decided a bag isn't so bad. Maybe when I can justify needing one, I won't feel so embarrassed sporting a cart on the course. The 3 wheel push (not pull) cart is the way to go. I also love the long fabric pocket organizer. But the bigger it gets, the more course accessibility becomes a concern.