I think the long run is desired outcome. And if I had only one rat in the yard for three years, I’d be okay with that.
With regard to the rats in the power lines; there are actually two kinds of common rats; Norway rats, Rattus norvegicus, which are the big ones, and “roof rats”, Rattus rattus, which are smaller and are the ones that we domesticate as pets. They don’t tend to co-exist, because the Norway rats are more aggressive. The roof rats are sometimes dove gray and have white bibs and feet. They are excellent climbers, so that may be the ones you’ve seen.