If it has an open source license, it is 100% truly "free and open source". That's a good thing, not a bad thing! There's nothing magic about foundations or volunteer organizations that make some things more open sourcey than others. That's the beauty of it, the lifetime of the code isn't bound to the lifetime of whoever made it, for whatever reason they chose to make it or stop making it. It's just the license, not who wrote the software, and not why they wrote it. Everyone gets the benefit of their labors regardless.

Volunteer communities and nonprofits are no silver bullet either- they're great when they exist and function well, but they don't always, and are highly dependent on who's involved, how much, and why. If there's a big, strong, vibrant community behind something, that's a good sign for whatever that thing is, but very few projects rise to that level of centrality in people's lives. There's also no shortage of projects without funding which have terrible or nonexistent communities surrounding them. Usually good communities arise during the long tail of maturity, like years or decades after whatever it is has reached a plateau of collective usefulness. Good software leads to good communities, sometimes, eventually, but it generally doesn't go the other direction. Something has to be great for years before it becomes that critical and that supported of a piece of infrastructure. That's why it's good that open source is only a factor of the license, not who made it, not who maintains it, not why they maintain it, and not how it's funded. That's literally what is special about it and makes open source a useful and good thing.

If the governance is well set up from the get go I think this model is fine. At some point you need money to make quality software.