I am for them and against them. I don’t have any interest in the military shooters they keep pumping out year after year (the kind @KnightsHouseGames mentioned). But I like the potential offered by such games or at least the viewpoint. And I don’t think it has really been explored much yet.
Like you mentioned, Minecraft used the FP perspective and did a great job with exploring the possibility space. I’m not sure what @neoshaman means by character interaction but in general I am all for having more interaction in games and that is something I would like to see in a FPS.
But the same can be said for basically any games really as far as limited interaction. I don’t really care whether the game is 2D pixel art side scrolling platformer or a 3D FPS, third person whatever as long as it offers many interesting interactions.
It’s this area where I think games still have a lot of potential to explore. We’ve seen games explore gee whiz graphics for (well the past two decades or more), they’ve explored story telling, movie effects, etc. Some have explored richer interaction such as Minecraft but what I would like to see is just games in general explore that possibility space.
Of course, doing all of that is not easy. That kind of thing takes a lot of work.
As far as FPS in general go though I think just having some more variety would be nice. I enjoyed Total Invasion and its sequel Total Invasion 2 (both are free downloads on GameJolt) made by one person with programmer art. Just because it was a different theme.
Here is a WIP (which I don’t know if it was ever released)
I stumbled upon these when I was researching alternatives to Unity dev last year. They are done in something called NAALAA (Not An Advanced Language At All). BTW - The free download of NaaLaa comes with a tutorial on making a ray casting style FPS such as the above.
Also you can check out the 7DFPS (unfortunately doesn’t seem to be a thing anymore but who knows maybe they will do one again some year) and other FPS on GameJolt and other places from hobbyists and maybe find something fresh at least as far as story, environment, mission and presentation are concerned. Possibly some unique gameplay too.
So I guess… why do I like the FPS that I like… because of the potential they have. The simpler games are pretty fun just in themselves things like Blake Stone and such. They feel smooth and fairly fast. Instant gratification of kills. Dancing with enemies. Sometimes some basic interactions such as secret panels, doors and such. But in general it is because I always think maybe this new (which may be old) FPS I just found might surprise me and have something more to it. They have a lot of potential to be more than they are.