Because human lives are not fungible. If some guy somewhere else was gonna die and you make an intervention where I'm more likely to die then that doesn't work for me. I will oppose it to the end of my being (after all, the alternative is the end of my being).
That is, if you take all the deaths from sleepy drivers, drunk drivers, angry drivers and replace them with random chance then I can no longer increase my chances of survival by not driving at night, not driving on holidays, not driving during commute hours, and avoiding shoals.
Instead now you've taken my ability to increase survival and moved it into the base rate. Nope, I think I'd accept maybe a thousand other arbitrary people dying before I'd accept myself dying.
Sure, but in a democratic system with perfect information you should expect to lose the vote on your hypothetical "me vs 1000" trolley problem right? And in the absence of perfect information you'd I guess you'd mount a special interest lobby and hope for the best...
If it were me vs random one thousand and obviously so, yes. But fortunately, the Wobegon Effect makes it so that anyone can conceive of themselves being me (or even better, of themselves being better than me - considering I'm not particularly a safe driver).
It is precisely because it is democratic then that makes it possible for any individual to exploit human cognitive errors. An authoritarian meritocracy would not fall for those tricks.
Well that 1.00000001x would include all drivers. Including those that are tired, on their cell phone, drunk, see poorly, senile, high, distraught, unlicensed, pissed off, etc.
Do you really want more cars on the road driving worse than an average awake driver that's not drunk or looking at their cell phone?