Can I pop in to say I think readers can enjoy LOTR and bring their own interp to certain points, even if it seems to contradict “canon”. In other words, I think acsenray’s interpretation is a-ok, for what it’s worth.
Of course. Ignoring what the author himself wrote and making stuff up is half the fun.
No, I’m willing to be told I’m wrong, if I am wrong. 
You’re pretty much wrong, but not completely (IMHO). The only JRRT writing on the topic tangentially supportive of your assertion that I could find was from “Unfinished Tales”, relating to the disaster of Gladden Fields.
There, while being besieged by Orcs, Isildur states he had not attained the power or the strength of will to don the ring in order to command the orcs, and he despaired in his own foolish pride for not destroying it when he had the chance.
This has always puzzled me. Given the uncertainty and risks of reigning in Middle-Earth, I’d think you’d want to improve your odds of having the royal line continue by permitting inheritance by and through women, as well. (The Imperial House of Japan is facing a similar problem now - lots of daughters, none too many sons. There hasn’t been a reigning empress since the 1700s, and current Japanese law forbids it).
Of course, thank you, Qadgop, for your customary thorough and well-written answer.
In the days when kings were expected to personally lead their armies into battle, reigning queens were rare. Women like Eowyn were quite uncommon.
Female succession had other hazards. Scotland, Navarre, and Sicily all lost their independence because female succession allowed one man to inherit two thrones. When Sicily regained its independence in the 17th Century, it adopted Salic Law specifically to prevent that from happening again.
One scary thing about Tolkien’s history: Every time the Dunedain changed their succession laws, a couple of centuries later some catastrophe would wipe out a large portion of the royal family. The ruling branch of the family would die out, and the new heir would be someone who was a direct-line heir to Elros by the new rules of succession. It was as if Eru was making sure the succession laws were followed to the letter, even if it meant retroactively wiping out vast swaths of the Numenorean population.