Player characters need advantages, because they're expected to kill dozens or hundreds of enemies between checkpoints. That's generally not fun if the PC dies in one shot, unless it's an excessively stealth and patience based game. Or dying doesn't reset progress, like in Unreal Tournament.
And a FPS needs lots of enemies in order to have any length of gameplay. The closest exception would be something like ARMA I guess, where there's a lot of tedious travel between the relatively few incredibly deadly enemies. Which is realistic, and apparently fun to some.
This.
Ultimately, there are two kinds of games that don't really thrive on making the player feel empowered: Horror, and stealth (kinda). For almost every other game, the player is there to feel like a badass. In CoD, it comes from mowing down waves of faceless mooks. In Nethack, it comes from finally getting the Amulet of Yendor. There are exceptions, of course; Dark Souls is a bit of a special case, blending stealth's thing (Being far weaker than the enemy, but getting through regardless) and a dose of standard empowerment, and with Dwarf Fortress, it almost seems to draw more from horror's form of enjoyment (HOLY SHIT EVERYTHING IS FUCKED FOR EVER, AND THE MOST I CAN DO IS MAKE IT MILDLY LESS FUCKED). However, most games still thrive off of making the player feel awesome.
As such, this usually means fighting very large amounts of enemies, and winning. This is absolutely insane if the computer is evenly matched to the player, because that means that there's an approximately 50% chance of the player losing in any encounter against a single foe, and becomes higher with more foes.
Now, do most games take it too far? Almost certainly. I'd prefer to fight less enemies but die faster in most FPS games over lots of enemies and apparently being made of titanium. But you can't expect a game to have equal strength players and enemies, because that results in extremely difficult gameplay that will probably just yield a ragequit, a crushed controller, and a shattered TV.