Prop trees are usually just a trunk and the lower few branches, as generally on stage sets, one isn’t looking up at the ceiling.
How much of the tree one sees depends on the set – hence the palm tree with receptacles for additional fronds. Since this particular palm tree is located outside a set window, we only see the bottom few fronds, so why bother to rent more? No one will ever see them.
Except the crew, of course, and we don’t count.