I'm not an expert and I can only share what I've experienced and how I feel about planks. As I consider my running, I can only say I feel it has helped. Before I was a bad posture runner, my shoulders were curved, my back was not straight and I probably used more energy then I should by my posture. I know when I did any hill work, I would slump into myself, and again waste energy fighting my posture. That is the problem with bad posture and running, you waste so much energy trying to get around. The posture becomes the problem. The reason, the core is not strong enough. Without a strong core, too much energy is being wasted fighting the posture.
Now when I consider my posture, I notice I don't have the rounded shoulders over hunched over back. I also notice that when I straighten myself up to run up a hill, there is more power. My arms swing without limitation. In other words, I don't feel I'm fighting myself when I run. I wouldn't use words or phrases such as 'graceful' and 'seemingly without exertion' to describe my running style, but I do feel that extra energy being used. I'm not fighting my posture any more. At least that's what I feel when I run. I'm not claiming any scientific study or truth in what I write, but my experience has changed as I run.
Perhaps the key is found in the phrase, I'm not fighting my posture any more. As the core is made stronger the posture does change and I'm able to use the energy to push forward or push up. A straighter posture seems to work through all parts of the running experience, either on the straight or on the hills.
I give no scientific data or explanation to any of this, all I know is, my core is stronger and that has helped my running experience. I will continue to do Wall Planks.