I think the actor and director were trying to honor Alan Moores depiction of the character(s). I don't remember the difference (if any) between the presentation of Kovacs and Rorschach in the film. But in the comic there is a difference.
The answer to this question is shown gradually. But I think the answer is:
From April 1966 - 1975 Kovacs was playing at being Rorschach; Rorschach had Kovacs voice. In 1975 Rorschach found his real voice. This is why he talks the way he does.
This is why I think this is the answer (I use the original source material in this discussion, because it was a reference that the movie cast and crew used):
The Watchmen comic uses talk bubbles to show the changes that occur to the way Rorschach presents himself outwardly. Kovacs took on the persona of Rorschach prior to Rorschach being "born". Rorschach was at the first ever meeting of "the crimebusters" in April of 1966. In the comic he is shown speaking in this meeting with a regular talk bubble with complete sentences and proper grammar.
While speaking to Dr. Malcolm Long in 1985, Kovacs (with regular talk bubble - and grammer slightly better than Rorschach) describes a kidnapping that occured in 1975. A six year old girl named Blaire Roche. This kidnapping is the catalyst that turned Rorschach into a separate personality, at least that's how Kovacs describes it.
The pivotal moment occurs when (spoilers / possibly disturbing imagry below):
Rorschach finds that she had been killed and her body was fed to two dogs (Barney and Fred).
Rorschach finds the dogs fighting over her bones. He then kills the dogs by splitting their heads with a meat cleaver.
Kovacs: The shock of the impact (of the cleaver into the dogs skull) ran along my arm, Kovacs said "mother" and closed his eyes. It was Rorschach who opened them again.
after that every illustartion of Rorschach's dialogue is shown in a broken talk bubble, with poor sentence structure and poor grammar.
However whithout the Rorschach "face" Kovacs is shown talking in a different tone.
I would say from April 1966 - 1975 Kovacs was playing at being Rorschach. In 1975 Rorschach found his real voice. This is why he talks the way he does.
additionally his voice is described by Laurie "Jupiter"