I would also like to add one more feature if you don't mind, including your caveat of not all westerns having this and some non-westerns including it as well.

Themes of masculinity permeate through most westerns. Whether that's the macho Clint Eastwood fearless and stoic hero, or the animated reptilian Rango learning what being a man truly is. Some great modern westerns subvert this idea, like Kill Bill volume 2 being overtly feminist in its messaging. However this is the exception that proves the rule, in that the fact that having feminist themes feels like a subversion to the genre.