Flatpak is a utility for software distribution and sandboxing. And that is what it does. Sandboxes are a means of isolating software from the rest of the system and each other. By using Flatpak to install software you deliberately choose not to choose the version of the browser that would have been tied into the rest of the system… And now it isn’t tied into the system…
This is “only on Linux that” part once again. I wasn’t comparing in the way you think, I’m comparing in the sense that cohesion and important details aren’t usually a thing when it comes to the desktop Linux experience.
Apple also has sandboxing on both iOS and macOS and this situations weren’t ever an issue because, back then in 2009, when they “developed” the technology they took their time to think about the implications and provide APIs and other ways to allow things to work. Flatpak is great, I use it and like it but it was also blunt “we just isolate things and fuck it” from the start.