System Shock never attempted to be just an FPS, though.
But that's the point - 90s devs were seeing how the FPS formula could be expanded on, especially in the realm of storytelling (or "
phenomenological possibilities", to quote Gabe Newell) while many throwback shooters seem to want to do the opposite and reduce it down to something even more basic than Doom. It took less than a year to go from Doom to System Shock.
Even if you don't class SS as an FPS - which I'd disagree with, it is an FPS, in the same way Deus Ex is - you can trace the lineage of games that clearly use Doom as a direct inspiration, and see a lot of experimentation and innovation going on, especially when it comes to storytelling or creating the experience of occupying a coherent virtual world. Marathon, Dark Forces, Descent, Hexen, CyberMage, Strife, PowerSlave, etc. Even fucking William Shatner's TekWar, the worst game ever and a total cash-in by the hacks at Capstone, was interested in experimenting with things such as a running subway system, non-lethal weapons, and a morality tracker (where FMV Shatner yells at you for shooting civilians).
Though I've somehow drifted into talking about mechanics when I'm meant to be talking about story/setting/art direction. Whatever, same thing, you can see how all the games I just listed were interested in those things too. Pretty much as soon as the FPS genre was born, LucasArts tried to make a Star Wars movie in it, Bungie tried to shove a weird cerebral sci-fi novel into it, and Raven tried to make a dark fantasy dungeon crawler.