Certainly not in spare time. It has to be part of the daily work. I compare it to running a restaurant. Cleaning up the kitchen every night takes time but it has to be done no matter the circumstances. You can't skip it or the health department will come after you. Unfortunately in programming you can get away with taking shortcuts for a long time.
Incidentally, good cooks are extremely tidy, they clean obsessively as they go - and they are under insane pressure, and don't wait for management to allocate time for cleaning.
They clean continously, not primarily to make the end-of-shift cleaning easier, but because it allows them to execute faster, better and more consistently (which in that environment is a necessary condition for executing at all).