A couple months back on the European Tour (maybe it was the Swedish Masters) there was a player who had no caddy and was seen on Golf Channel using a trolley (pull cart). I might have heard of somebody doing it at Q school as well.

Is there some rule that I cannot find concerning tournament golf as it pertains to the use of a trolley in high school, college and bigger amateur tournaments?

I love to walk and rarely ride in a golf cart, in fact I consider golf a different game when riding in a cart. To each their own however. But walking 18 or more holes while carrying a 20-40 pound "carry bag" seems that it must definitely be harder. So you compromise and leave out all but the bare minimum and have a "lightweight" bag or you carry everything you may need on an 18 hole round like the pros do and have a 35 pound bag.

So what gives? Why is nobody using a pull cart especially in college and high school golf?

I used a push cart this week at the US Mid-Am, so the USGA allows them. It usually depends on the tour or golf association as to whether they can be used. I'm playing in the state Mid-Am later this week, and they are NOT allowed. That's probably because the course wants you to ride so they can get the cart money. The USGA makes you walk, so there is no cart money issue.
I loved using the cart this week. It takes very little effort to push the cart around, much better than carrying the bag!

A push/pull cart is for sure the next best thing to a cady if you can't find one. It all depends though on the tournament and who is running it.

better than most caddies...

DB

In junior tournaments they are not allowd you have to carry your clubs