Because const correctness quickly becomes an all-or-nothing process in games.
If you start enforcing it in a few places, suddenly you've got functions needing to ensure they are const so they call other functions and those need to be changed. Then it starts to propagate and you've got some library you don't control that operates on a read-only fashion and should be marked as const but isn't, so you need to take steps to fight const correctness because of the third party library.
It quickly becomes an all-or-nothing proposition. If you are providing a library it is less of a choice: be const correct. If you are using libraries and all of them have been careful about that, wonderful for you. But if you re using a bunch of other libraries and any of them are not using it, it quickly becomes the stuff of nightmares.
In practical terms, the main benefit of const correctness is a benefit to the programmer. It can help identify and prevent certain bugs, but assuming other good practices are in place those bugs will be prevented anyway by code tests and code review and QA testing.
Ultimately the options boil down to complete const correctness through the code base or completely avoiding const in the code. In most projects I've worked on professionally, teams have chosen the avoidance route primarily because attempts to reach const correctness are blocked by external libraries.
And now I'm emo. I hope you're happy.