>so distant from daily routine that it seems completely pointless

imo, this is a problem with how it's taught! Order theory is super useful in programming. The main challenge, beyond breaking past that barrier of perceived "pointlessness," is getting away from the totally ordered / "Comparator" view of the world. Preorders are powerful.

It gives us a different way to think about what correct means when we test. For example, state machine transitions can sometimes be viewed as a preorder. And if you can squeeze it into that shape, complicated tests can reduce down to asserting that <= holds. It usually takes a lot of thinking, because it IS far from the daily routine, but by the same rationale, forcing it into your daily routing makes it familiar. It let's you look at tests and go "oh, I bet that condition expression can be modeled as a preorder on [blah]"