Some of them also don't meet the requirements either - it has to be a single player FPS.
Personally I'd quite like to see omg aliens are invading

Duke Nukem Forever looks like just my cup of tea.
In terms of environments I quite like globe-trotting titles where you get to see a whole bunch of different areas. Something like C&C Renegade was pretty cool in that regard. Games based too much in only a couple of difference environments (e.g. Doom3) can be offputting if that particular enviornment isn't to your tastes, it's good to have some variety.
One of the key factors for me is having a good variety of weapons and enemies too. I like to feel like most of the weapons have a use, rather than just sticking with two or three. And crucially, I would ban any lame-ass contrived crap happening half way through the game where all your weapons and ammo get nicked due to capture. Or, if that had to happen, I'd make sure when you recover it it's exactly as it was before - I like stockpiling ammo!
Moving on from there, I like bosses which can be killed by conventional means if you have enough firepower, rather than needed some silly trick to activate the crusher, telefrag them, activate a laser or any of that nonsense. If I've been careful and saved up 14 cannonballs, 87 rockets, 1000 chaingun round, maxed out on grenades, 40 railgun slugs etc I like to feel like it was worthwhile, I wanna say "Come on then you ****er!" and unleash my arsenal on that behemoth in front of me. I wanna wear them down and chip away at their 5000hp until they bite the dust. The one good thing about SiN:Episodes was it has bosses like this.
I think there is definitely scope to bring in RPG elements as happened in Deus Ex, and maybe we should have a party system too. I've love to be able to move around with a small squad of AI teammates, who actually have decent AI but are also controllable by the player. X-Com Alliance looked promising in this regard back in the late 90s but sadly it was canned. So it would be a bit like KOTOR combat except realtime and first person.
In terms of scale and open levels, I think the Deus Ex series has it about right. You can move around towns etc reasonably freely, but it's not so bad that they get hideously lost very often. I think where FPS are concerned being too open-ended can be a bad thing for some players like me who like to be guided a little. I don't want to run around endless back alleys trying to work out where the hell I'm supposed to be going (NOLF2 was a little annoying in this regard).