I agree with almost everything you wrote:

Crysis vs. Far Cry. Yes, I still did not buy Crysis, Far Cry was just better than the demo of Crysis promised. I could just play and it still looks very good.

Bioforge: This was a great game, I am still waiting for Bioforge 2, the end of the game promised a second part. It was so movie-like at this time, what a nice feeling to be part of this sad and deep story.

Unreal 1: I love this game. It was so much better than Unreal 2. The mixture of fantasy and sci-fi, the story, the beautiful peaceful world in contrast with the evil invaders. The Nali were such a nice race, helping me on my journey. The setting was so varied. The balancing was fine and technology was just impressive at that time.

Quake4: Here I have to disagree. I enjoyed it to be a part of the game, not the über hero. I very much liked the missions with some marines helping me, lighting the darkness with their flashlights. It felt a bit more real to know that I am not the only one, that I am just part of a big invasion. I got the same feeling in "Star Wars - Republic Commando" and I really like the AI of the other commando members, taking strategic positions for sniping, grenade launching and so on.

HL2: I think this game and the following episodes are very well made. It is still an old-school FPS but contains a lot of extensions (placing turrents, using pheromones, vehicles, solving puzzles, using physics). But every new element is introduced so carefully, you find hints to solve puzzles everywhere. This game is made for everyone. You can get the idea how they did it if you replay it with comments of the developers. They really tested the gameplay a lot and balanced everything after this.

Bioshock: Did you realize that they tried a lot to make it easy, more easy than System Shock and co? And it helped, they sold much more units now. You can play it like a shooter, you can just follow the arrows in your HUD to find the next goal and you can ignore all the special magical abilities, the turrets and the tricks like burning oil, electrical shocks in water.
So it offers both: a simple shooter layer and a more advanced layer for people who like to dive deeper in it. This approach is quite good.

And now I compare the old games often to the new FPS games. What is happening now? If I hide behind a rock then all my life energy comes back, magically. I dont get into this. It just feels so fake.
Then all these new games use third person views for shooting around corners. This breaks the idea of FPS and also feels strange to me.

I really would like to have the budget and time to be part of a project similar to the first Unreal, maybe smaller, with a few nice extensions and modern visuals. A short prototype would be enough for the first run.