In a sad way it is a relief in that the mountain lion is a very dangerous animal higher than us on the food chain. Hiking in country they inhabit has always been a bit of an adrenaline rush whenever an unexpected sound or rustle occurs. They'll attack you from above ... a rock, a branch ... and, unlike grizzlies where the danger is usually that you surprise them, the feline is the one springing the surprise.
Never seen one in the wild but once in Big Bend NP, where there are warnings posted at many trailheads, ran into a party of hikers, one of whom captured a photo of a cougar standing in the trail ahead of him and just watched him until the rest of his party caught up and the cat, respecting that it was outnumbered, high tailed it out'a there. I was happy to be hiking in the other direction.
Another time in Wyoming I was standing in a trail admiring a handful of mule deer who were brousing in the nearby brush. Suddenly, an ominous rustle spooked them and the next thing I knew they were standing on the trail about 10 feet away from ME looking up into that same brush. We (me and the deer) all stared for a short time before everyone relaxed and went about our business but I can say that I had certainly felt like a cat myself as some primitive instinct not quite evolved out of my system caused the hairs on my spine to stand up straight, or so it felt. I happened to record this on an old camcorder I was carrying around at the time and, well, there's nothing to see here folks so let's move on but the emotion of the commotion is captured as another priceless memory of the mountains.
Those who mourn the "extinction" of the cougar may perhaps take some comfort in knowing that they exist in suitable habitat and, on the brighter side for northern New Englanders, the lynx appears to have recovered and is now being consider by USFWS for removal from the "threatened" list I think it is.