Steam has been surprisingly network share compatible for years: I keep all installed Steam games on an SSD based share on my Windows network server on a 10Gbit or rather NBase-T network.
Not only does it allow me to run the games on various other computers without installing them locally, it even allows me to play them with the various different user IDs in the family.
It's not perfect, mostly the games themselves aren't perfect, but it's certainly much better than giving every computer enough SSD capacity to hold a full stash of games.
Biggest issue is that sometimes file access across Windows network shares is just terribly slow. My favorite game (ARK Survival Evolved) is also one of the worst, because it has literally thousands of tiny little files, which take ages to load.
E.g. loading a complete session from scratch can take minutes on even my fastest NVMe machines with 8-16 core Ryzen 3 CPUs, while loading the same game under Linux from a HDD is noticeably faster!
That only gets worse when you try to load it using Windows shares, but other games with just dozens of [larger] files don't suffer nearly as much from the network overhead.
And it is 10Gbit networking, with 900MB/s transfer speed when copying VMs...
So now I tend to keep the really sensitive or incompatble games locally and the majority on the share to balance things. I need to play with attaching and detaching network shares to ensure games stay where I want them, but I've gotten used to that.
Because of the network and file open speeds issues I've seriously considered running all my gaming PCs on a Linux base with KVM and GPU passthrough to a Windows guest OS and using Linux for the shares (CIFS/NFS/Gluster), but I never seem to have enough time to test all of these variations for compatibility and performance..
Unfortunately all the other shop clients, Uplay, Origin, EPIC, Oculus can't hold a candle to Steam when it comes to really valuable features like this!