PHP Composer and DTAP
The above mentioned environment is almost impossible.
Of course your question is why?
Composer (try to) install(s) packages and makes installation on every environment.
So you need to run composer on every DTAP environment!
But that's not always possible.
The DTAP environment has the simple idea that an installed version can be copied from Development to Test to Acceptance and Production.
But Composer needs to be run/installed on every installed environment.