If I live in a society that is keen on regulation, then I feel more safe doing things. I can not have information in my head about what all is regulated and how much. When I do things in the US, I feel safe (relative to known risks), because I believe we are a high-regulation society (feel free to argue that). If that image starts to slip, then I have to start asking myself: Should I take my kids on this helicopter ride at the county fair? Should I go down this remote cliffside road on public transport? Should I get in this old elevator? Should I leave this electrical appliance running while I sleep?
Maybe it's a little thing in the big picture, but some people value it immensely, and many Americans appear to be those people. Declining to regulate deep-sea subs, or whatever else, maybe doesn't have any practical effect, but it is one little chip out of the image of high-regulation.