Going back to more general thinking on realism in games, not just BF2...
I don't believe the question should be "should games be realistic?", but actually "should game X be realistic, and if so, how much?"
Realism is a sliding scale when applied to games. Perhaps the ends of the scale of "Simulation" and "Arcade" or something similiar?
At the simulation end of the scale, you are attempting to emulate reality in every respect.
At the arcade end of the scale, you are only interested in entertainment.
Games commonly sit somewhere in the middle regions of this scale. Pure simulations can be tedious, heavyweight affairs, requiring weeks of training (just as in real life) and even then suffer from their controls or visualisations -- after all, a monitor, keyboard and mouse, plus perhaps a joystick, can only go so far to emulating real life. "Pure" arcade games can be exceedingly abstract, but even then often borrow from real world principles (gravity, simple harmonic motion, elasticity, etc) in order to give them understandable properties. I'm not sure it's actually possible to have a game that has nothing to do with reality... (I'm ready for ideas though!
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Battlefield 2 tries to pitch itself a little past the middle on this notional scale. It wants to show real world things but doesn't concern itself with many real world problems -- bullets don't cause fixed damage, a single 9mm round is enough to kill you stone dead, injuries should slow you down and disorient you, vehicles don't explode quite so spectacularly and certainly don't "unspawn" their destroyed carcasses, etc, etc, etc.
Action Quake 2, if you're familiar with it, deliberately pitched in at the less-than-realistic end of the market... action movie physics and mechanics were in play, as much as the Q2 engine could manage.
America's Army works on having realistic elements to it, but it's just not fun being sniped by the guy who's played this map for the last 100 hours... again and again and again and again... sure, it might be realistic, but I just don't find it fun.
I think critical factors in designing a realistic game include considerations on how long it will take a person to pick up the basics, how well the raw mechanics work
within the game (as opposed to compared to real life), how much real world experience can be safely/properly used within the game paradigm, and how the game handles "the death penalty".
Death, in games, is a crucial element. Counterstrike says, "Die and you're out". Action Quake 2 did the same. Battlefield has gone with "Die and you're out for the next 20 seconds... oh and you're back at some respawn point too". Planetside had a respawn counter and spawn locations. Most RTS games operate a "Die and you're out". Most MMOs operate a "Die and respawn somewhere safe, perhaps with some other temporary inconveniences". Unreal Tournament has instant respawns, albeit at your base. Even games that push for a relatively high level of realism, such as Red Orchestra, allow respawning.
Death and losing are important in games and how they are implemented directly affects how realistic one can feel the game is. Can a single bullet kill you? Frequently? Are there enough grenades in the game to allow for 'nade-spam? If so, does that mean loads of people can die at once? Once you're dead, do you have a short period (seconds) or a long period (minutes) or being unable to play? You can answer all those questions in different ways and suddenly you change the whole game-feel.
Possibility of one-shot-kills, 'nade-spam, and Counterstrike-style 5 minute rounds can lead to new players getting around 45 seconds play in any given 5 minute period -- that's 9 minutes play in any hour. In anyone's books that's pretty tedious, but it is pretty "realistic".
However, UT-style respawning combined with attrition-based damage (large health bars, low relative damage) and few area-effect damage abilities leads to slugging matches that carry little in the way of realism.
... and all that's just considering a single game style -- the battle.
Personally, I like games that vary around the middle ground, carrying sufficient aspects of realism to allow me to use some real world thinking at the game, but without requiring that I undergo weeks of training, read manuals that are an inch thick, or sit out substantial portions of the game because I haven't played it enough to survive yet.
Fortunately I started playing FPS's when they first arrived and so I've been able to step into the majority of them without much learning, but I've watched people step into modern FPS's fresh and seen how frustrating they can be, requiring prior knowledge of the map, excellent 3D-awareness and map navigation, fast reflexes, prior knowledge of "the best weapons" and, above all, the willingness to die frequently and without explanation until, at some point, you eventually figure out what you should have been doing all along.