If you run a third party that is appealing enough, you can certainly have a go at it. I just have literally never seen, I don't know, the Green Party put up a candidate for local city elections.
It's not like party establishments haven't had candidates lose despite all odds. And Independents have had good streaks at lower offices (e.g. Bernie Sanders, Michael Bloomberg)
Was responding to the idea that the Green party doesn't put up candidates for local elections... I think I've seen them on smaller races than Governor as well, but this was a recent example that came to mind easily.
It's not like party establishments haven't had candidates lose despite all odds. And Independents have had good streaks at lower offices (e.g. Bernie Sanders, Michael Bloomberg)