Some of you have a big problem with playing the wrong games. If killing shit might get to you...you might not want to play a game where a big part of it is killing shit.
"Killing shit," itself isn't the problem. The impact of killing being diminished — emotionally and mechanically — in games that are not about shooting/fighting at their core is the problem.
You see wave-based combat in games have a setting/style which suggests the developers originally wanted to focus on exploration, world-building, Etc. If the final game actually is centered on killing, said killing is low-impact and incongruous with the game's theme or setting. Fighting/killing hundreds of people — even in games in which narrative beats revolve around individual deaths — is so common in all major releases that there's a large portion of the gaming community that accepts this gameplay as being appropriate in games it's arguably out of place or overdone.
Ted Ken Levine mentioned in an interview that they had to shift focus more to Bioshock Infinite's combat during development, suggesting that combat wouldn't be as prominent a gameplay loop as it is in the final game. Considering the circumstances in the game, killing is not out of place. However, the game clearly wants me to care when a major character dies or enemy is defeated, yet after seeing so many die so easily by their own hands, those "important," deaths are cheapened, as are the hundreds caused by the player. Worse yet, the main story beats in most games of this type outright ignore the player's actions, allowing said actions to feel even less impactful.
From a purely mechanical view, killing hundreds of quickly dispatched enemies is a simple way of garnering engagement for the player, but not necessarily the most appropriate. Games like RDR, GTAIV, Tomb Raider and Bioshock Infinite feature mortal main characters. They can all take all manner of deadly attacks that would mean instant death in one of these game's cutscenes and they also kill literally hundreds of enemies who are, canonically, as mortal as they are.
The further into the above games you go, the less likely you're able to recall individual moments of combat or individual kills. Rather than each kill being an intense encounter or distinct victory, it's just filler. Each of these games too frequently feature mass battles and each enemy is so braindead and easily dispatched that combat is only interesting/challenging when there are dozens of them.
What OP, Bedlam and others in this thread are trying to figure out is a way for games to make killing meaningful in games. That doesn't mean that
all games should have only four enemies in a game that each put up as good as fight as the player and each leaves the player remorseful/introspective. However, if a developer wanted to make a game like that, there should be a feasible way for them to accomplish that and people shouldn't automatically think there's something wrong with the game for having little killing.
Parts of Max Payne 3, and Kane and Lynch 2, have fights that I felt were appropriately graphic and difficult, relative the game's world, game mechanics and story. There's a shit-ton of killing in those games, yet there were only a few parts where it felt incongruous and forgettable (on either a small-scale/moment-to-moment basis or long-term).
Even when it felt like too much, the feedback — enemies/objects reacting to being shot, sound design, Etc. — made each death have impact in the moment; death was appropriately graphic/disturbing. After some battles in those games, I wasn't merely glad to have completed the section, I was relieved I didn't get (virtually) killed. Metal Gear Rising: Revengeance does a decent job with feedback since you're able to use a "1:1" slashing mechanic and cut things up directly; the player is able to be more involved with what's happening on the screen, so instead of just tapping a button until the enemy cyborg is dead, you actually slice his arms and head off. This happens hundreds of times throughout the game, yet the game is focused on combat and killing each enemy is an involving, graphic experience, something that's also addressed in the game's story/by its characters.
There's one massive flaw in your argument OP.
IT'S A VIDEO GAME!
You are over analysing it.
He's over-analyzing it if his only concern is to merely enjoy absolutely everything that occurs in a game. He wants this aspect of game design to be improved though which will require some analysis beyond "it's a game."