And - oh man this is a negative rant I'm so sorry! - I still play DOOM for nostalgia reasons. But if I'm playing a new shooter, then I want mouselook, textures that don't look awful on my 22" widescreen, etc.
I would like to add that the reason oldschool FPS games were such a big hit is more because of their technological revolution (texture mapped 3D graphics, multiplayer) than game mechanic, content, or gameplay.
Take Doom for example; everybody went crazy when it was first released, but after Quake was released, suddenly Doom became obsolete. Quake has better graphics and multiplayer, while graphics and multiplayer are what Doom is all about. So after Quake was released, why would people play Doom anymore?
It is a much different case with, say, System Shock. Yes, its graphics are obsolete compared to Quake, and it has no multiplayer at all. But there are reasons why people would prefer System Shock than Quake, because it has more complex gameplay, intriguing storyline, and adventure/puzzle-solving elements that Quake doesn't have.
Yes, my Doom example above is probably flawed; people would probably stick with Doom because it probably has better content and plot (or what passes for plot) than Quake, but if that's the case, it actually supports my point; that if two games have exactly the same kind of "pointing and shooting" gameplay, but one has better graphics, then the one with better graphics win. And that's the reason I don't play old school FPS anymore.
But MasterM, regardless of what I say, it is still your project after all. If you want to create such games - simple FPS with vintage-style graphics and no plot whatsoever, then please go on. Like Gemini000 said, you will gain a lot of experience, learning, and probably have some fun while doing so.
But if you ask others whether they would play and enjoy such game - a game where you just running around and shooting things without any plot whatsoever, then I doubt the answer would be 'yes'. I, for one, wouldn't play such games anymore - not while there are a lot better FPS out there. Even with upgraded graphics (tried GZDoom some weeks ago), Doom feels boring and repetitive compared to Call of Duty. Yes, I played it for a while out of nostalgia, but after few levels, I got bored.
That's much different than, say, Ultima Underworld. Even with the likes of Skyrim out there, Ultima Underworld doesn't feel boring and repetitive. And despite its primitive graphics, I still enjoy re-playing it again after almost twenty years. I do not play Ultima Underworld - and many old games, for that matter - for nostalgic reason alone; I play it because of its great storyline and interesting gameplay.