There's definitely risk out on the roads even if all engines went away. My best friend was killed in a car accident a few years back (no buggies involved, only an unlicensed 15 year old running a stop sign). Another was hit by an impatient driver trying to pass while she was making a left turn. She lived, but was yelling at the first responders to just let her die because she was in so much pain. It's not really that buggies are dangerous, so much as the fact that *we endanger others* every time we get behind the wheel of a car (which I still do as well, unfortunately). It's just so commonplace that it doesn't register anymore.
At least with the buggy, your own speed is much less likely to do you in. Other advantages... people don't take frivolous trips, because harnessing up the horse is kind of a pain in the rear. 20 miles is about a max range, with 10 being much more comfortable (which is why areas developed before cars typically have towns spaced 5-10 miles apart. Big hills are something to be avoided at all costs, whereas they're not even a consideration in a car.
Perhaps the biggest thing we lost when we started speeding around in cars is community. All of a sudden people could live anywhere far from work and family, and move on a whim, so that's the new norm. That's precisely why the Amish refuse to own cars, because their community is central to their very existence. We're all anonymous behind the glare of our windshields, and are travelling so fast that nobody would have the time to recognize us anyway. I can't count the number of times I've thought, "Who's this ass riding my tail?", when my thoughts (and the other person's inconsiderate behavior) would probably be very different if we could see and recognize each other.
On this website, people clearly have an appreciation for older ways of doing things; it's not all just ramping up the challenge and thus the reward. I suspect that very few people know what they lost with advent of the automobile though.