“Should there be better security.”
No. There is the moat to keep the people and animals separate. The whole point of those types of exhibits is to make the viewer and the animals seem to be on the same "field’ so to speak. more invasive barriers would ruin it.
That and would it stop a determined person? No, they would just need to wear bike shorts under their dress to scale a fence. If you did make a fence that would hinder people climbing it, with say razor wire at the top, then again, you destroy the whole aesthetic.