I use Fedora (KDE) and game a lot. While I mostly like it, I’ve had some problems with it that were non-trivial to solve, so if you’re a Linux beginner I would not necessarily recommend it to you.
Perhaps Bazzite would be a good option? It’s based on Fedora and created with gaming in mind. I got it recommended here and installed it on a friend’s kid’s computer and he’s very happy with it so far.
There’s also Nobara which builds on Fedora to create a gaming-focused distro.
My guess as to why this isn’t a more central feature of Linux distros is that this is not something most users need. If you need to reinstall the OS because you broke it, then a full system backup is probably more convenient, even if it’s less than optimal to back up packages which you could download. If you need to reinstall the OS because you want a clean slate when upgrading to a new version, then your package list for the old version could cause a lot of conflicts as maintainers regularly remove and add new packages.
I have backed up my zsh, vim, tmux, etc. configs and written a few shell scripts which install them and download vim plugins etc. If I ever need to reinstall the OS I would use these. However, in the last 20 years since I ditched Windows I have reinstalled Linux exactly two times: Once because I was an idiot and didn’t have a proper backup when I accidentally formatted the wrong HDD, and once when I switched from Xubuntu to Fedora in which case a package list wouldn’t have been usable.