Apologies for the long post:
<<both the individual game and the genre>> Surely enough, but I get lost in trying to understand the catalog of "genre." Somehow, the player has to be an active force in the game, correct? In the simplest gambling device, the player at least has to drop a coin in a slot. So the third person in the Batman game is like a puppeteer?
What I mean by genre is how it affects choice of viewpoint. For example, the strategy genre generally works much better in third-person or overhead view - including most of the city building games we play. Of course there's games like Trenched on Xbox and Sanctum on PC which are a mix of strategy and action (fairly simple tower defence games) which nevertheless work quite well in first or third person. There is also the Uprising and Battlezone series, and Hostile Waters: Anteus Rising, which have quite a bit of strategy in them but are played from 1st or 3rd person (and games that work like this are very rare). It would be, however, highly difficult to play a game like Civ in 1st or even 3rd person view.
As a clarification, I see 1st and 3rd person views as controlling an individual entity, as opposed to overhead or strategic view where you control any number of different things.
Here's my take on common genres and their common views:
Action - 1st, 3rd
RPG - 1st, 3rd
Strategy - Overhead
Adventure - 3rd
Sports - 3rd
Simulation - 1st
A sim game (as in simulating the experience of driving or flying etc) lacking a 1st person mode would automatically disqualify it from the sim genre - it is seen as a highly necessary part of the simulation experience. Sports games are most often in 3rd person view even for those games where you play a single player on the team; the comparative lack of spatial awareness that comes with 1st person hurts the gameplay.
Personally I feel more like a puppeteer or director / influencer when playing a 3rd person game. Sometimes this is exactly what I want, it all depends on genre and playability.
<<sensation of living in the world>> Wow! This is the magic that the PC was supposed to provide which board games were supposed to lack. The board war-gamers (whether figures or chits) struggled to get players to "enter" the period and the limitations of sight and time compressed to the table top - etc. It was a dream of being able to look at a computer screen and see a reasonable simulation of what a unit commander could have seen on the battlefield and to receive information and to issue orders as the commander would have done. Somehow it doesn't seem to have gone that way.
Yes, unfortunately most games are still highly abstracted - if they weren't it would be necessary for a large amount of automation from the AI to be played in realtime; for example no real life battlefield commander tells each and every squad exactly where to go and what to shoot etc; they of course give general objectives but it is up to the squad leaders to carry out those objectives.
Most realtime wargames consist of telling a single squad at a time what to do while your dozens of other squads hold position. Or otherwise pausing the game every few seconds to tell each of your hundreds of squads what to do. The Total War series of games seem to handle this fairly well though.
It might be interesting to have a game that lets you set general objectives, similar to the Majesty series.
That sensation of 'living in the world' that I mentioned is for me personally very rare, and has only come with The Elder Scrolls games and some few others. I remember back in the 90's playing a rally game on the original Playstation where I found a nice hill and drove slowly to the edge to watch the sunset. Although the graphics were crude I still had that sensation.
The Need for Speed: Shift games give great visual feedback in the 1st person helmet cam views - the game is viewed as if through a helmet which has an actual physical presence, in that the driver is knocked and shifted around as the car moves or crashes. It is highly effective, though some people don't like it of course, but standard bonnet cams and 3rd person views are also an option.
The second Kane and Lynch game is an interesting case (although the game itself isn't very good in my opinion): you control your character in the 3rd person view, but the camera view is that of a person following along with hand-held camera, similar to the show 'Cops'. It has all the bumps and shakes that you get in real life, and is even dropped and picked up at certain points. It therefore combines immersive 1st person camera views with 3rd person control.
<<the topic of view preference>> <<grounds the player in the world>> <<the potential to interact physically with the world in a more realistic way>> I think you here reference only the first person, player as person and not puppet. I suspect making a pair of eyes looking out of a body at an artificial world takes a highly refined graphics program. Could it be that is why it is often poorly done, or just avoided -- defaulting to the puppet third person?
Yes, I'm talking about first person here. Generally it's actually fairly simple - you take the player character model and remove or hide the head, and stick a camera there. Even in games that use a simple floating camera for first person (which is most of them), there is still a fully complete player character model that the player never actually sees, but is used so that other players can see them.
One reason it is not done is so the developers can create high quality models and animations specific to the 1st person view, and consisting only of a pair of arms and the weapons. Nowadays though the overall quality of every art and animation asset is quite high, so I'm not really sure why more games don't work this way. Another possibility is that 3rd person animations don't always translate well into 1st person - a 3rd person sidestep can feel a little jerky or jumpy when viewed in 1st person to a player more used to the smooth sliding of a floating camera.
And thus concludes my 4am rambling.
(damn insomnia...)