It's the same answer to the question, Why does hot water clean better?
When water is hot, the molecules spread farther apart and move around faster. This allows the molecules to work its way in to dirty material and loosen it up. It speeds up the process of soluble matter in becoming solubilized.
So does hot water clean better? Well it cleans faster, which to many people is indeed better.
But that doesn't mean cold water can't clean, and in the same way, it doesn't mean cold water can't solubilize the flavors in coffee. But it is slower.
Another part of this is that the flavor of anything is different cold vs hot. Some people prefer hot to cold coffee and so out of convenience just hot brew instead of going through the trouble to brew it cold and then heat it up.
I'd also argue that cold brewing vs hot brewing extract different proportions of acids/tannins/flavors, and that you can brew with varying times/temperatures/pressure to get the proportions you prefer. You may like the proportions that hot brewed coffee gives, but want to drink it cold (such as iced-coffee). Or the reverse, cold-brewed served hot.