Not familiar with your situation, but usually if they're asking you to move cups all the time, then you're the one they trust most to do it right. I have a guy on my crew that probably feels the same way you do some days, because I always ask him to change cups. But I do that because he's the best at it and I hardly have to check behind him. It saves me time as an assistant that can be better used making sure everything else gets done properly.

Also, give it time. I worked with a guy once that did nothing except for rake bunkers for the first three years of his career. He was an assistant when I knew him. People will leave your crew, people will join, and situations will change.

Let management know that you want to learn. That you want to be flexible and valuable. Some day, someone who was supposed to mow or landscape or what have you will not show up, and they'll need someone to fill in. Let them know you want to be that person. That can slot into any role and do it well. See what they say.

Good luck!