Ingrained dirt actually justifies a thorough cleaning by specially trained staff on regular basis because I would not see myself permanently cleaning my working place for the sake of "absolute" cleanliness and I am not there for that.
However, self respect and respect to those who are taking over from you is a matter of good education. Some do have it, some others just do not.
As usual, and it's deplorable, the only way to compell people to clean up after their duty is sanction.