

I see how the website gives that impression, which I assume is an attempt to push non-technical users toward an install method that does not lead to support requests and helps fund the project.
The site also mentions that you can build it from source for free, so it’s not technically claiming that it’s only available from the Play store. If you follow that link, you’ll see that availability on F-Droid is prominently displayed on the README.
Flatpak is great for two groups of users: the ones who only use default settings in standalone apps and the privacy-oriented experts who know how to tweak things to their liking. In the middle is a large group of users who don’t know or care how things work, but they want that one feature an app is supposed to do but mysteriously doesn’t work with flatpak.
Even one of these occurrences is enough to make most users give up on that app or the OS entirely. I like the idea of sandboxing apps, and I use flatpak daily, but we have to acknowledge and hopefully improve some of its limitations or many users (yourself included, it seems) will consider it unusable.