We trellis tomatoes on our 6' chain link fence and our chocolate cherry tomatoes overtop the fence. The tomatoes they *might* do better with the taller support. We grew beans (I think) up two 5' plus tipi-like trellises. This year we are growing peas on nylon cord strung between the fence and a 30" fence post and will see how that works.
Looking at the photo I like the construction with extra bracing at the corners. Gives me an idea how to rebuild the garden gates.