I don't believe Uber has the kind of relationship with its drivers that you're suggesting. From what I understand, Uber drivers are independent contractors and determine their own working hours and working days. I also had the impression that Uber drivers can turn their "available" signal on and off at will. So many of them run their own private car companies and switch the "Uber available" app off while handling their own rides. They're required to accept rides only when their signal is "on".
Moreover, I think you're underestimating an important effect: which is that significant events like snowstorms, maybe sporting events will affect both supply and demand. The impact may not be something that anyone can forecast.
When the Uber surge price rises to 6x normal, new supply will enter the system, and demand will leave it. Say an Uber driver is relaxing at home and did not plan to work today. He receives a notification that fare is now 6x normal. That will entice him to work today, even if he wasn't planning to. Or a driver that works predominately in a different area might travel to the area that needs more drivers. Etc. The fact that price can fluctuate in this way ensures that sufficient supply is available. The high price literally creates supply. There is no economic incentive for a taxi driver to come into work on his day off in order to give rides in a snowstorm if he'll receive the same prices the following day.
Similarly, when the price rises to 6x, Uber users might decide to call a friend for a ride, instead of taking an Uber, ensuring that people who have alternative means of transportation use them, leaving the drivers available for those who wish to pay or have no alternatives.
Thinking through all the side effects and eventualities, the fact that price can fluctuate according to supply and demand provides a significant benefit in the way of allowing more rides to occur.