The biggest sticking point is not the heating of the coffee at all, it’s the widespread misunderstanding of the what the word cold means in the term “cold brew”. It is incorrectly assumed that brewed relatively cold (room temperature) means served ice cold. Somehow a lot of people can’t understand the verb brew has nothing to do with serving temperature. Does that make sense to you?
Although you are entirely correct in a technical sense, and it's common to serve hot brewed coffee cold, the opposite is so rarely desired that it will be considered 'weird' (in the sense of 'unusual') 9 out of 10 times.
Every extra process involved in making a coffee is going to add complexity and time to the workflow, which many cafes will elect to charge extra for.
There is some consternation in Australia about paying more for iced coffees compared to hot ones too:
I know, I know. You’re right. But… even if it is weird, it is so easy! It’s not really the default assumption that’s frustrating, it’s when I get push-back for a request that is normal and default for other espresso drinks, something trivially doable, something every barista does dozens and dozens of times a day.
If hot cold brew was common you wouldn't pay extra for it