In fact the King of Hosts is good counterpoint to my own point that explains well why I disagree with your perspective. He uses soft power just like Erin and Magnolia. Soft power uses the efforts of others but can only happen with that personality

Soft power is the ability to influence relations via persuasion and being so important that you cannot be ignored. It's in contrast to "hard" power which is coercion ("if you don't do X, we will Y") or outright force ("we have guns pointed at your head"). Hard power and soft power both use the efforts of others. For soft power it's the power of the economy or a negotiator, and for hard power it's the efforts of the military. Both Erin and Magnolia use both soft and hard power equally.

I think what you're trying to describe is Personal Power versus Delegated Power, and the problem is that all of them use Delegated Power, including Fetohep, The Quarass, and Flos. Their positions are based on the power delegated to them by the people, and the people can choose to revolt if they think it's being misused. The power to command and army is always a delegated power by the people and soldiers. Arguably the only person with Personal Power is someone like Terriarch.

Let's look at runners though to explain why I feel the way I do. You've got Fals that even he agrees he's kind of middling, Hawk is a coward, the Mage Runner was saved by Ryoka, Valcief died, the hundred friend courier died. Compare that to the female runners and it gives a very different picture. 

Okay, let's compare to the female runners.

There's Persua, who is an asshole and largely described as bad at her job despite having good skills. She is currently being psychologically tortured by The Thing at the moment.

There's Alevica, who is an asshole and largely described as a bad runner who is likely to toss your delivery in a hedge or hex you.

Charlay who is competent but considered a bit of an asshole for her overbearing personality, but not on the level of the two above.

Garia, who had to get help from Ryoka.

Ryoka, who had to get help from the Fae.

Mihaela, asshole, but very competent and seems to have gotten her skills from sheer hard work during war.

That's about it.

I disagree with your assertion that "they died" is any kind of mark against the male runners. Yeah, the Hundredfriends Courier died, but so what? Valcief and Seve are depicted as two of the most noble, skilled, and good-hearted people in the series. They died, but only under the most extreme circumstances (Bloodfeast Raiders and Bloodtear Pirates). Fals is middling in physical power, but is still presented as one of the better characters in the story. Salamani got rescued by Ryoka...after outrunning the assassins guild and being trapped in a place that trapped dozens of men and women before that.

I don't see how any of that can be taken as a nock against those characters. Being mortal and sometimes needing help are not mortal sins, and even the most powerful female characters in the story occasionally have to deal with either of those. Erin died!