There is a difference between the way a tradition murder mystery handles the perpetrator and the way a serial killer mystery does. A bloody topic to treat so lightly, I realize. However, murder mysteries in their core construct represent the very basics of all mysteries, however nebulous the "crime" and/or the "perpetrator" be. As J.J. Abrams remarked, "Mystery is the catalyst for imagination." And imagination is very important to creativity.
In a traditional murder mystery—or "whodunnit" mystery—the identity of the perpetrator in all its parts is kept strictly a secret. A series of clues mixed with misleading evidence teases the audience with a list of suspects. For this to happen, the audience must first meet the suspects. This must be a group of people equally capable and motivated to have carried out the act—at least at first, until suspects are eliminated by new information.
To reveal that the actually killer is not a person we had met, is to have cheated the audience out of any hope of figuring it out. Incidentally, to give the audience so much information about the killer that they do figure it out is to disappoint them. A good whodunnit delicately balances the audience's desire to solve the mystery themselves with the desire to remain challenged to the last.
By contrast, a serial killer mystery is a different animal. Unlike whodunnits, serial killer mysteries like "Se7en" aren't so much about "who?" as "why?" Typically the motivating factor for the detectives is a question of "when?"—as in "when is he going to strike again?" A story of this nature becomes a thriller as they try to determine the "why?" in order to get ahead of his plan and stop him.
"Who" a serial killer is, is a "serial killer." He is defined by his MO. In other words, the real villain of these stories is not a person at all, but the diabolical plan he is executing. In this way, the structure of a serial killer story has much in common with any conspiracy or manipulation story, regardless of the presence of impending murder. When a construct is laid for a large plan which is destined to wreak havoc (by design or because of flaws) similar methods of profiling the purpose and ideology of the perpetrator(s) is used.
Therefore, this type of story tends to open the door to deeper levels of philosophical implications. In the case of "Se7en" (affiliate link) the killer's plan is to make a demonstration of the "7 Deadly Sins" of Catholic literature. The film itself invokes Dante's Inferno (affiliate link), and makes a similarly gruesome display of sin and punishment. The irony is that the killer is acting as a sort of dark angel, delivering "God's message" through sin itself—even though I rather think the creators drop the ball at the end when assigning him the deadly sin he is guilty of.
All-in-all the point is that to be fulfilling and long-lasting, fiction must involve the viewers in the process of the story. Furthermore, it must lead them to areas of thought previously unexplored. This is the essential fascination with mysteries. Superficial mysteries of the "Clue" variety make for fun entertainment, but soon all seem alike. No matter the number and style of twists, "who" is still just an average person—boring.