@SwampDonkey If you keep visiting lots of zoos, then you are bound to come across some open-topped exhibits for those big cat species.
Just looking at cougars/pumas, I've personally seen open-topped exhibits at the Greater Vancouver Zoo and B.C. Wildlife Park in Canada, while the U.S. has zoos such as ASDM, Chattanooga, Cougar Mountain, Dakota, DeYoung, Northeastern Wisconsin, Northwest Trek Wildlife Park, Pine Grove, Living Desert, Shalom Wildlife Zoo, White Oak and Wildlife Prairie Park that all have cougars in open-topped enclosures. That adds up to 14 different zoos. Plus, I could add some European zoos to that list, such as Pairi Daiza and others.