We do, but we get "spins". When a distro starts they accidentally pick a core desktop environment by simply picking one first. They call their distro Foobar Linux and everyone is happy. Later people realize that the choice of desktop environment wasn't good for everyones needs and they add a KDE spin called Koobar Linux or Foobara Linux or who knows what else worse unrelated shit they can call it.

The end result is that most users who are getting involved in Linux for the first time are making this choice long before they even know they are making this choice or being given an option simply by picking a random letter version of a distro like Xubuntu or Kubutnu or not having a letter at all and it being Ubuntu alone.

There are a few distros that have done it better and given the user a choice upon install to pick their DE. OpenSUSE has always done something like that from what I recall and I appreciate it a lot.