It's kinda hard not to have deaths in a story where the monsters are all about ritualistic murder.
I've yet to see Blade, Agito and Hibiki, but compare that statement with later series and try to realize that THAT is the almost usual monster's routine.
Either that or exterminating humanity, replacing humanity, enslaving humanity, eating humanity. Etc.
All in all though, to me, a series's "Realness" factor comes from characters having emotions. It definitely doesn't come from redshirts dying. I mean seriously who cares about redshirts?
That's an out of place reference.
A red shirt is someone that is already known to die shortly after entering the scene, already marked for death, a pawn.
It happens so often that it becomes expected.
Random mass murder is something else.
The 'reality factor' is that in one of the first episodes there's a police officer saying something on the lines of:
"If we count the cops, 240+ people died in a week, guns are useless".
In most other series police is avoided or already fighting the baddies (look at Kabuto or W).
So there's a lot of people dying, and people talking about it. Even the police is scared. That's a lot more realistic than a lot of... nothing going on in other series. (to the point that you start wondering why there's no police around, ever).
There was also an episode about a litlle girl's (potential) suicide.
It's still Ep 12 and there's more mature stuff than what entire series did later.