What is the use of making dinosaurs poop in Ark?
Solution 1:
There are two use-cases I found for the making your dino poop:
1. Fertilization of Crops
As @DisplayNameNotFound describes in their answer, poop can be used to fertilize your crops. The larger the poop, the longer it fertilizes.
You can feed your dino and then ride it in circles to make it poop faster.
2. Preparation for Escape
When riding on a dino, it needs to stop to poop. This doesn't take long, but when chased by a raptor or something, this can cost you some precious seconds.
If you wait too long, the dino will poop by itself - and running (e.g. from an enemy) consumes the most energy. Therefore, whenever I'm exploring and I see my dino ready to poop, I trigger the command myself.
Solution 2:
Fecal matter from your dinosaurs is useful.
Taming time varies from food to food; it takes nearly nine hours to tame a max level T. Rex using raw meat, but just under 2 with kibble. Fecal matter is useful for, indirectly, making this kibble, by using the feces as fertilizer. Acquiring the poo can be useful for taming.