I've seen them close up and was not scared for the reasons you mentioned, it wanted to be seen. I had a slightly scarier incident where I was hissed at from thick bushes by a mountain lion that I couldn't see, but I left and the lion did not follow.
It's extremely common in our area for lions to attack and kill small dogs and livestock. For that reason, there aren't many people that appreciate preserving these animals even though there have been no recorded attacks on humans in our area.
Bears used to be common in the area too, but were hunted to extinction hundreds of years ago and the ecosystem adapted and survived.
If lions weren't here there are lots of people who would definitely hunt to keep the population down.
I think people overestimate the danger of lions to people, but also overestimate the environmental impact if they left.
But overall I know many people who have seen lions up close or been followed while hiking and everyone ended up being safe.