Surge pricing, alternatively know as dynamic pricing or price gouging, is a form of price discrimination and takes on various forms. Brian Albrecht does an excellent job of covering what it is. I would suggest you read his blog, even if you think you know what surge pricing is.
However, what I want to talk about it is why exactly people think surge pricing is unfair.
In some ways, we don't mind price discrimination if it benefits us. Happy hours in bars for instance or when you get an off-peak train tickets. However, I am not sure people view this the same as price gouging. These prices are upfront and transparent.
I think the situation most people view as price gouging is when you go into a store expecting a certain price, and suddenly they are much higher. This is especially the case if you made a special trip to the store on assumption of paying that price.* If prices become unpredictable, it would likely have a negative effect on demand for your product anyway (this is similar to the brand loyalty argument of why firms do not price gouge).
Alternatively, if you go into a store and see a huge queue, you might still be annoyed, but you are not going to start ranting about this being grossly unfair like you would if the store was price gouging.
On the face of it, waiting in line, and price gouging are not so dissimilar. Those that have a greater desire for the good are more willing to wait in line or pay a higher price. Even though waiting in line still incurs a cost (time is, in fact, money) I think there is a difference.
Waiting in line is seen as the great leveller. It doesn't matter how rich you are, you still have to wait in line (although it does favour those that are time rich e.g. pensioners). So paying a high price for busier periods may not reflect your need for the good, but your ability to pay.
From here, you could go down the rabbit hole over the efficacy of surge pricing but ultimately, most people simply think surge pricing is unfair (even after you have explained the logic).
A taxi driver could theoretically charge someone a lot of money if they were dying and needed to go to the hospital. But most people think this is asshole behaviour. As a society we want to discourage asshole behaviour for a variety of reasons. It is why people reject offers they feel are unfair in the ultimatum game even if this means turning down free money.
In economics, what we deem as fair or not can be viewed as a preference and preferences are what determines demand.
So the simple reason companies do not offer surge pricing is because it is not profitable for them to do so.
Getting annoyed with people that think surge pricing is unfair is like getting annoyed with people for preferring apples over oranges.
* Perhaps this is why people don't get annoyed at Uber so much as you can just simply check the app on your phone and potentially make other travel arrangements if the price is too high.
