I agree with your premise. But I think it’s not even necessary to find specific arguments like this for why surge pricing is OK.
Surge pricing applies to the vast majority of products and services in our society. It’s supply and demand. It’s capitalism. Houses in more desirable negihborhoods cost more than those in less desirable neighborhoods. The Metro in Washington, DC costs more at rush hour. Hotels cost more when there’s a convention it town. When there’s a shortage of oil, the price of gasoline goes up. When there’s a drought, the price of food goes up. We seem to accept all these without a thought. It makes sense. When there isn’t enough of something to go around, the people who want the absolute best you can get right now (a hotel walking distance to the convention, a steak when there’s been a bad year for cows) should pay a premium. Those who don’t care as much can pay less and have something worse. Everyone just doesn’t get the exact same stuff as everyone else.
So I don’t understand why anyone thinks that a premium transit service — an on-demand ride, between two points of your choosing — should be any less subject to market forces. There’s no basic human right for a taxi. We don’t fix the prices for food and water, or pretty much anything else, why should we fix them for a ride that you order with a smartphone?
Artificially limiting the price of a product (transportation) that is in limited supply is bad for society. It provides no incentive for conusmers to decide if they can accept an alternate as you say — waiting, getting a ride with someone else, doing a rideshare instead of solo ride. It puts everyone in the same bucket (people who REALLY need to get somewhere NOW, and people who don’t care that much). Demand pricing encourages people to decide how important the ride is.
When you REALLY need to be there right now, you will surely be glad for surge pricing, because without it, you just wouldn’t get there.