Having children is a choice, and sometimes people back themselves into untenable situations. You can't use children as an excuse to put the lives of others at risk. Realize what you're saying here.
People driving cars they can't afford to upkeep are also risking themselves and others.
Yes, it sucks. I empathize. I shouldn't be throwing stones. But if I'm a juror on a vehicular homicide case I'm not going to think less of deaths that were caused because the defendant had children to take to school. It would be more compelling than a DUI case, but it doesn't bring people back to life.
Obviously this line of thought has devolved pretty far from the original point as someone who can afford a car with driver drowsiness detection can probably afford to make different choices. It's just the idea that no one should ever drive when they have even a slight risk of falling asleep seems quite unrealistic, at least in the US.
Personally, I can find myself a bit tired by the end of the day. I've never felt at risk of falling asleep while driving, but I'm human, so can't say with certainty that it will never happen. Maybe a driver aid will lull some into driving when they know they shouldn't, but I still think it will be a net win (just like seat belts).