I'm gonna say differently
You don't need a cart but you do need something that will survive a blowing rain. Get or build yourself a smaller box that will hold your bench stuff and your good to go. Put your stuff in the box, carry it somewhere near your next bench, and you're good to go. I used some kind of waterproof plastic box for years (Rubbermaid I think) and found it was far less trouble than a cart. The difficulty I found was locating a box that was the right size to hold my stuff and it not slide around...but not a big problem.
I found that I could throw my stuff in the box, clamp on the lid, pick up my rifle, put my case box under an arm and tote the box to the next bench area without having to wait for those with carts to get out of the way. I had an old MTM case box that was worn such that the lid stayed fully open and that was just the thing. Mentioning that because it needs to be mentioned as that could be the difficulty involved. You think you need something better or more sophisticated and it often becomes a problem at times or places. If you can shoot the Super Shoot without a problem, then you can shoot anywhere.
Carts are a problem in every aspect. Go to win...not look good.
BTW - Make certain that if it comes a blowing rain that you're covered in every aspect. If you go to the Super Shoot three times, you will encounter a blowing rain twice. When I say blowing...I mean just that.