> Why not charge a little bit more during off peak times, and then turn around and incentivize drivers using the subsidy from off-peak hours, rather than dumping it all on individuals traveling during points of tumult/crisis?

Because someone else would start up with a pricing model of charging less during off-peak hours, providing no service whatsoever during weather situations, and the pricing model would fail.

It can be done at the government level - tax cab rides, then use the proceeds to subsidize those at other times, but it can't reasonably be done by one company unilaterally. The medallion system sort of does this, by fixing both price and supply. It's probably suboptimal, though.