elliot's role
Elliot is a major character in the series, so of course his role is a very important one. Along with Olivia, he is one of the two detectives that the show primarily focuses on (so let's call them the dynamic duo, shall we?). The airtime he and Olivia get tends to outweigh what we see of the other detective team. Even when compared to Olivia, I think Elliot
gets a bit more airtime. Since he is the only character with a large family, he is the only one who can have that kind of backstory, and a major setting outside of the precinct.On that note, it's undoubtedly Elliot who is the 'family man' type of character on the show. Olivia, Cragen, and Munch do not have any kids. Olivia has never been married, Cragen's wife is deceased, and Munch has had several unsuccessful marriages and is currently single. Fin, however, does have a son that we get to see on occasion, and although Olivia's mother makes an appearance in the pilot, she passes away in season 2. But none of them compare to Elliot as far as having a large family. In some cases, this is a good thing for them, because the nature of their jobs would certainly interfere with family time, as Elliot knows all too well.
Additionally, Elliot fills the 'tough guy' role on the show. Granted, none of the other characters are real softies, but Elliot is raw and gritty, and his over-the-edge attitude has even served for side stories on the show. The role he plays is likely meant to symbolize the anger and contempt that we, the audience, feel toward the disgusting and despicable criminals on the show. When he pummels a perp or smugly tells them to enjoy their new life in prison, he is also providing us viewers with a sense of satisfaction.