In economics, "surge pricing" is actually called "pricing"
This is all just supply and demand. When there's a snow storm, supply of taxis shift left, causing the quantity to fall and price to rise. The movement along the supply curve towards a higher price coaxes some taxi drivers onto the road who would not have been willing to work at the previous lower price--this is good for customers, who would not otherwise have any transportation!
Now, certainly there are lots of people who will not want to pay the higher price. Of course they don't! That's the whole point. In addition to increasing the supply relative to the old price, we have movement up the demand curve, so that the quantity demanded is lower than it would be at the old, lower price. An intuitive way to see why this is fundamentally a good thing is to observe that people who need the taxi services more urgently--to go to the hospital, for example--will be willing to pay more than someone whose needs are less urgent--for example, someone who needs to go to the comic book store. If the price does not rise, there will not only be less supply, so that even fewer people get taxis at all, but there will also be no sorting mechanism to ensure that high-urgency needs are met first. Without "surge pricing" the second guy might well get the taxi to the comic store, leaving the first person without a way to get to the hospital (my suspicion is that an ambulance is even more expensive than the "surge prices!").
The general lesson here is that the purpose of prices is not to reward or be fair. They convey information that coordinates supply and demand. When you institute a price ceiling, as in the graph, you are implicitly telling consumers that there is a lot more supply than there really is. It is no surprise, then, that when we have price ceilings we get a highly inefficient allocation of resources across the economy.
Of course, people will still feel that Uber is making unfair levels of profits out of this. That may be so--I do not know anything about their finances. But the solution there is not to prohibit surge pricing--which hurts everyone--but instead to simply tax Uber's unfairly high levels of profits. We can use the revenue to lower everyone else's taxes. Like the second fundamental theorem of welfare economics says, Pareto Efficiency is compatible with any distribution of income. But you gotta get the prices right.