However, after playing with it, checking out their board of directors, and deconstructing their app design, their vision is not really "cloud storage", at least, not the way we typically think of it.

Their long-term mission is preserving a digital legacy, oriented around relationships, families, and organizations. You don't use permanent.org to store things in the cloud that people normally think as "cloud storage", not for the day-to-day stuff. The kind of things you want to store in there are the things you want the world and your descendents to have access to after you die. They won't have to (directly) pay upkeep to keep that legacy preserved. I think that is convincing enough for me to see it as a critical piece of free and open web, even if this doesn't seem obviously connected to the idea of preserving a legacy.

For example, an indie musician wouldn't have to rely on SoundCloud to keep their recorded music around. SoundCloud is not in the business of preserving the creative work; they are in the business of aggregating users and they use user content to do it. Placing those music files in permanent.org has a much better shot of preserving that creative legacy for future generations than leaving it on SoundCloud.