All I can really think of is Bad Company 2 with the Frostbite 2 engine. Harvest Day with Javelins in the mountain? Awesome.
I mean, if I could make any game I wanted, I wouldn't make an FPS. Maybe a 3rd person shooter or something kind of like Killzone Liberation for the PSP. Heck, I probably wouldn't even make that.
I know what I'd like to see story-wise in an FPS though. A story of a platoon of men, fighting a valiant rear guard effort in a losing war...where one by one everyone dies...except for one squad that's incredibly lucky+skilled. That squad is sent on a series of secret missions where stealth and accuracy are key. While on these missions, they uncover a conspiracy of sorts where they find out that their platoon is one of many and that they were intentionally given the shitty missions to whittle them down. But, now they're winning the war because of strategically important missions. So now you the player are left with the choice to continue fighting or to go AWOL and now you're wanted.
The first half of the game would be a lot of large scale combat, a la World at War. You get standard issue weapons and a standard issue kit and no special abilities or cool gadgets. Also, the first half is more like...idk, CoD MW2. No helicopters beyond being scared shitless by one and then watching it get blown out of the air by [insert Deux Ex Machina]. You gain a lot of experience points for doing cool stuff but you never get to spend it. Here, you deal with the strife of losing your friends. Lots of interesting characters that get killed off one by one. I'm thinking Kat from Halo:Reach and Ghost from MW2. Those deaths were sudden and unexpected and personally, had the most effect precisely BECAUSE it was unexpected.
Until the second half, where it gets a lot closer and personal. Here you spend those points on special abilities and weapons. Instead of a 4 standard kits for an average guy, you have 4 classes with unique kits. At this point, I'm thinking Delta Squad from Raccoon City. Add in the aggro mechanics from Army of Two and I think you'd have an awesome game. Lots of sniping and stealth kills. In this half, you deal with the betrayal of your platoon by the government. Like General whatever his name is from MW2 except on a larger scale.
PS- Hmmm...also, I kind of want the player to be able to customize his platoon. Kind of like the different battalions in EndWar. Let the player pick which battalion and which company he's in. And banners. I want there to be company and platoon banners that the players get extra points for defending/capturing.
The setting for this? Could be modern day. Could be near future or sci-fi. Could even be WW1! Vietnam! This story is pretty genre neutral. Open to modding, even on consoles. Sort of like the Indie section on XBLA.
Interesting, it seems I came up with an FPS I'd like after all...
PPS- OH and multiplayer. Your standard Conquest game but I'd include something from Crossfire (probably the only good thing about that game too); Ghost mode. Fucking LOVE Ghost mode and I'd have that in it too. Dino mode maybe (I like the idea!). In Dino mode, you have to defend a compound from the dinosaurs...call in Artillery on that herd of Ankylosaurs! Pterodactlys in the sky? Call it in for the F-16s! Essentially Horde mode with dinosuars and on a bigger, chaotic scale. Infection mode but on a bigger scale too. 22 humans and 2 zombies. Low lights, lots of shadows and the best defensive position is at the very end of a medium sized map. Lots of little well defended locations that all have some hard to defend/see location for the zeds to get into. Multiplayer is where it gets funky.
PPS- Another MP mode I wanna try out. Predator mode. In predator mode, you have 1 Predator. He's invisible standing still, semi-visible moving, and you can hear him breathing. He has a 4 shot sniper rifle. When he shoots, he's instantly visible for a couple seconds and there's a contrail to his position. Other than the 4 shot rifle, he has melee. The Predator's objective is to eliminate all opposing team within a certain time. The opposing team just has to survive. Bonus points to the Predator if he wins in a set time (30 mins overall, +100 in 10, +50 in 20, +25 for winning period). Bonus points to the other team for living. Last man standing gets +100 and down from there (2nd to last gets +95 or something, I haven't done the math). The points received in multiplayer can be used in singleplayer.