That's a tough one. I can appreciate the merits of studying them. However, justice (in whatever form) should be the first priority.
An aside; In my opinion, proficient serial killers seem to have a commonality. That is a belief in their own superiority and intelligence over law enforcement. They all seem to relish in their duping authorities.
With that in mind, how can they be studied? It would seem to me that they would continue their mind games - especially once incarcerated. Instantly they have nothing beter to do other than thinking, planning and rehearsing.
Reminds me of Bundy. Right before his excution, IIRC, he started talking about how pornography was the root of his evil, in hopes they would stay his execution. Didn't work.
Watching how they play their mind games is, in itself, very telling of the mind of the serial killer. Glean all the info, then let justice take its course.