yes!

I grew up in KS and assumed it was just something like "don't do something stupid and let the animals out", but this makes more sense

Growing up in KC when I heard jt it always had the connotation of “leave the doors as they are”, but when I heard my family in Tennessee use it it had that implication of “these doors are the way they are so animals don’t get out” so I think you’re in the ballpark

yes, it's also to rotate grazing through different pastures sometimes you want a gate open! this is for a murder mystery party, so we want some rooms kept open for the game, some doors kept closed only when in use, and the yard gate kept closed, etc etc