You might be being a bit of an idealist there...
Middle-earth was a dangerous place. The Elven-kings rarely had times of peace (except for in the time of Gil-galad, who was like the Queen Victoria of the Elves). As it were, the mightiest of the Elven kings, like Fingolfin and Fingon, fell in battle. If they could barely hold an office, how would a woman be able to hold the office? There were a few exceptions (i.e. Galadriel and Aredhel) but generally, I believe that Elven women were weaker than the men. Women just couldn't do it. At best, they would have been able to command the defense of a kingdom, but even that was pushing it. The only cases of a woman defending a kingdom, or playing an integral role in the defenes of a kingdom, were of Melian and Galadriel. Melian was a Maia and Galadriel was one of the greatest of the Elves, so they weren't exactly the average. They were most definitely the exceptions. Even then, they still only played a part in the defense of their respective kingdoms. They didn't go out and command forces. They left the dirty work to their husbands.
Heck, I'm a woman myself, and I acknowledge the fact that sometimes it takes a man to complete the job.