If a zombies core function is to just kill and eat meat, they would just all end up constipated and unable to eat anymore, amirite?

Zombies are in a constant state of the slow runs. This diet is what keeps them regular.

There are animals out there that exclusively eat meat. These animals do poop.

In SNK titans puke once they get full, I guess zombies could do the same

There are professors amongst zombie s and they might use a pencil

If you give the zombies miralax they tend to feel a lot better over about an hour, much more docile

you're talking about core function, not secondary function. Who knows what else they can do in the back-end