My husband and I made many trips to Big Bend and other wilderness locations with our daughter, and there is a resident cougar where I live and hike now-I avoid areas the cat is known to frequent, and I do not let my dog and cats stay outside in the yard like food to go. Coyotes can also be extremely dangerous, especially in packs.
Lesson #1 for enjoying the wilderness is to not hike alone, make plenty of noise, don’t run or ride a bike-triggers predator response-and carry mace or a sidearm. That said, it sounds like the cougar that attacked the child was rabid-it needs to be put down, and I’m guessing that is what the Parks and Wildlife people will do. A healthy cougar does not normally grab a person who is not alone, according to the game wardens and other wildlife people.
Cougars will go after people, especially small children when they are desperate. usually from being sick or injured.