Oh, if only Gary Larson would have continued “The Far Side.” Picture a herd of cows standing upright by the roadside. Each cow is wearing a cloth trash bag over one shoulder. One cow turns to another and holds up a hoof. “How are we supposed to pick up trash with no hands?”
Years ago, I was renting a house and once noticed a bird (not a crow) up on the roof gutter pulling stuff out of the gutter and dropping it over the side. I was all in favor of this, because the gutters tended to get full (there was a tree that overhung the roof). Couldn’t make a deal for him to do it on a regular basis though.
I read your “solution” with Dwight Schrute’s voice, and it was perfect that way.
Off the top of my head, I bet that if the gutters were full of wet plant matter, they were probably also full of all kinds of tasty insects for the bird to find.