I wouldn’t say it’s gaining popularity so much as it’s just becoming the new norm, you know? Multiple distros like Fedora, PopOS, Elementary, etc. allow you to install applications easily from their repos or from Flathub. They’ve always been popular with developers as it takes far less work to ship their application across multiple distros/DEs. As a PopOS user, you’re going to want to use flatpaks for anything that you want more up to date than the repos that PopOS has, which pulls most of it’s packages from it’s Ubuntu base. As a Fedora user, some applications are only available as a flatpak, so unless you want to build it from source yourself, its just easier to grab the flatpak version. As for an Arch-based user, most will grab something from the AUR if it’s not in the main Arch repos.
In my use case specifically, I first tried using a system with zero flatpaks, and just relied on the Arch/AUR repos for everything, which works fine and everything I needed was available. However, that does come with a headache or two from time to time. I’ve run into a handful of AUR issues or errors, which were all solvable and helpful to learn more about the AUR no doubt, but it’s not without it’s drawbacks.
I had like ~40 packages or so from the AUR, updating and maintaining them was a slight learning curve, but manageable. When I tried Fedora 36 recently, I had to use a few flatpak apps and while this might be anecdotal, I found some of them to perform better than their AUR counterparts had that I was used to using. So I decided to swap out any AUR application I had for a flatpak equivalent if it existed and after doing that, I slimmed down my AUR package count to about a dozen, which is much more manageable. I also slimmed down some of the other packages I’d normally have like electron, java, etc that I don’t need save for one application using them.
For example, using Tauon Music Box (great music app btw), from the AUR, pulls in a lot of python packages, both from the Arch and AUR, an amount even the dev has acknowledged it’s getting a bit out of hand. With the Tauon flatpak, I don’t have to worry about this, and it updates the same since the dev maintains the flatpak version too. Overall, I like what I can get from the Arch/AUR repos, but it doesn’t bother me any to grab a few flatpaks here and there to make my computing time easier.