Consider the unwanted side effect: If there is a message followed by logout, you'll never get to read the message. I actually disabled clearing the screen on my Linux machines for just that reason. Hint: In /etc/systemd/system/getty@.service.d/noclear.conf, add TTYVTDisallocate=no.
Using the same logic, the best place to implement clearing the screen after logout may be in the configuration of getty: See man getty and man gettytab; a quick search didn't find anything that leaps out, but please read them more carefully.