Whenever possible, I buy from GoG, but not because I want to use Galaxy. With GoG, I just download an exe, run the installer, and my game appears in this wonderful launcher called The Freaking Start Menu. It's great.
What do I get from using a client? I don't want my games to be integrated into a social network, I just want to play them, and not be interrupted until I'm done.
------
My second choice after GoG is usually itch.io, but my third choice is actually becoming EGS. I'm not sure if this was intentional, but a significant portion (maybe even a majority?) of EGS games don't actually need EGS to run. You can download them with an open-source tool like https://github.com/derrod/legendary, back up the files, and run them. I've personally done this with Journey, Beyond Two Souls, Control, and Detroit.
A handful of Steam games allow this too (one recent example is Ori and the Will of the Wisps), but it's much less common than on the Epic Store!
Big picture mode, controller mapping, remote play, and remote play together are amazing.
Not sure what's so hard to understand. You mention downloading, installing, and revel that it's in your start menu. And don't mention updating. With launchers, there's one less step (installing), and updating is a passive thing (for better or worse). And yup, they're placed in the start menu as well.
Single player games purchased a year after release likely never need to be patched ever again.
Unfortunately AAA games with multiplayer et al seem to need to be patch immediately upon release...
Their work with the Proton compatibility is bringing a lot of my old Windows only games to Linux too. I'll probably continue buying exclusively from Steam for this reason.
Recently I've started using OS search to launch apps on my Ubuntu workstation. One day I've tried the same with game launched. When you have extensive libraries on multiple platforms it definitely helps.
Also some clients support achievements. It adds incentives (or meaning, if you will) to play some good game even after completion of campaign or something like that. Yep, not for everyone.
BTW, you can download and install games from Steam using official console client [0]. Not sure if will allow to play [all] games, though. I had limited experience with that. I managed to download windows versions of doom and quake 2 for Oculus Quest from Ubuntu.
Yeah, SteamCMD can download but usually not run games—my experience is the only games that run are the handful that can run without Steam in general.
Only the app from GOG shows games from other platforms, that's why I prefer to launch everything from there because when I launch my windows rig on weekends no chance I remember where I bought that game.
Also, to install games from those 3rd party platforms one still needs to install and launch those platforms. So this limits usefulness of the Galaxy.
[0]: https://www.gog.com/galaxy