Why isn't there a Pyramid Head in Silent Hill 3?
Because SH3 is a sequel to the first one, and as such Pyramid Head wasn't needed for that story. His appearance in SH2 and Homecoming is meticulously crafted for the characters. Unlike in the movies, Pyramid Head is not a guardian. He's an omen and manifestation of guilt or revenge depending on the character. Silent Hill 3 was ultimately a twisted coming-of-age story that explored themes of body autonomy and self-ownership. Conversely, Silent Hill 2 and Homecoming instead explore themes of accountability and atonement. There isn't anything Pyramid Head could have added to Silent Hill 3 from a narrative standpoint and as such, he wasn't needed.