Earlier quoted context omitted.
Why is it not banned?
It is in the land of the free. It's generally not banned in Europe, so most BASE jumpers who are active spend at least a few weeks a year there. About 10 to 20 die world wide in about a population of 1000 or so active jumpers. It can be done relatively safely but the group isn't big enough to regulate effectively and most BASE jumpers are hostile to anyone mentioning the idea.
It is in the land of the free
I'm aware that BASE jumping is banned in US National Parks (and it's been argued that this increases the risk [1]), but it doesn't seem to be banned generally in America (see Perrine Bridge, or Bridge Day, for example [2]).[1] https://www.theguardian.com/sport/blog/2015/may/22/did-rules...
[2] http://www.nerverush.com/base-jumping-locations-plan-jump/