Why are planes allowed to fly with just one pilot?
Well I guess there are multiple angles to this. Perhaps someone can chime in with reference to regulations, but I can offer a more pragmatic answer.

Like it or not, aviation, like many other things, is a trade-off between risk and cost and I think that's what it boils down to. So what is the risk of single-pilot incapacitation and what is the potential consequences versus what is the cost to have all aircraft have at least two pilots aboard (not withstanding the impracticability of fitting two people in most single-seater aircraft.

So, I guess, we as a society have accepted the risk of single-pilot incapacitation and it seems that mostly the consequences are acceptable compared to the cost. It would be unlikely that we would mandate against single-pilot cockpits, but where to draw the line between single-pilot and multi-crew aircraft is certainly an on-going and active regulatory discourse.

In the end, I could ask you why don't we mandate two people with two steering wheels in cars? It would certainly prevent some accidents (hell, maybe many!), but it could also cause some too. And, practically, it just isn't going to happen is it?