I don't know if I'd go as far as to say people are "risking their lives" on cheap tires. For all the millions of tires out there on the road rotating millions of times every day through all kinds of conditions - many of them being of the "cheap" variety, how many do you see failing? Tires, no matter what quality, seem to be very reliable. And if they weren't, we'd know about it. Every manufacturer has their low-end, people are buying them, and it's not harming them physically. They may not last as long, and people may abuse them, but they don't seem to fail.
On the other hand - I just had a $175 Michelin tire fail on me on the Interstate at 70 mph. To me it looks like a sidewall failure as there is no evidence of trauma to the sidewall of the tire. All I see is what looks like the tiniest of pinholes in the main tread. There was nothing in the road that I ran over that I could see (9 AM, clear day). So why did the whole sidewall fail instantaneously like that? Michelin did a massive recall on these "Latitude" tires a couple of years ago for sidewall defects, but these tires came after that. Did they correct the problem? Maybe the recall didn't extend far enough? Michelin told me to take the tire to an authorized dealer, but all I got from them was either "You need to take that up with Michelin directly" (Town Fair Tire), or "that's not a sidewall defect, but I can't tell you what it is, either" (Sears), So even "higher-end" Michelin has had dangerous defects in their tires. You just never know...
Well, I guess you couldn't make the balancing machine "idiot-proof" because ultimately the tech has to hammer on the weights and he could put them wherever he wanted - out of distrust for the machine, sheer ignorance, or even maliciousness.
What about changes to the tire over the course of its life? Wouldn't that potentially change the tire's balancing characteristics? You're on the Interstate, suddenly lock the brakes and skid 50 feet. Wouldn't your tires need to be re-balanced? You whack a curb, but there's no outward signs of damage to the tire. Does that affect the balancing?