I pretty much outright don't believe you. Flatpak ships by default on a lot of distros; it works on Linux Mint and is integrated with Mint's software center. In my procedure I said "click the first option that pops up" well the Flatpak version is the second option. I do know that Manjaro requires you to go into the software manager's settings and toggle it on, and Ubuntu deliberately doesn't include Flatpak by default because of their competing Snap store.

The assertion that Flatpak "does not come by default on most systems" is factually incorrect. Per this page: https://flathub.org/setup the majority of distros listed say that "Flatpak is included with newer versions by default and is ready out of the box." With a notable exception of regular old Ubuntu, for which the command is "sudo apt install flatpak." Or Arch or Gentoo, whose entire deal is "By default we install AS LITTLE AS POSSIBLE. Do it yourself."