What can be done to reduce such encounters?
In India, certain rural areas had numerous human-Tiger encounters that resulted in deaths especially of women going to rivers to wash their clothes. So the authorities deployed human looking mannequins that had an electrical current running through them. This way when the tiger attacked the mannequin, it got a severe shock from a jolt of electricity. It was a shock that was large enough to dissuade the tiger from attacking humans but not enough to kill the tiger.
Why can't Americans implement a similar system to dissuade bears, cougars and coyotes from attacking humans in running trails?
There's no reason to implement a specific system. Cougar attacks are quite rare. Bee stings kill people much more often. So does lighting. Realistically, these guys had terrible luck.
I've never heard of bears attacking runners. Black bears generally try to avoid people, and running into one is not as scary as most people seem to think.
By far the most dangerous, scary animal one is likely to encounter in the woods is a man.