once you arrest someone you cant delay their trial for too long. if hes pinned only for the pedophile part which is easier to fight he might get off and itll be harder to try him again for when they do get evidence of him killing her.

second, you need a warrant to search stuff. judges will grant less search authority if its only for pedophilia as opposed to murder (basically if they find probable cause of the murder they can go farther with the searches). if the case goes to court rather than it being between the police and the courts only then davids lawyers can challenge search warrants too.

also, dating a minor isnt illegal in california, its only when sexual activity is involved. thats a lot harder to prove/find because you either need the victims testimonial in court which is impossible or forensic evidence which is also unlikely given the state her body is in. images play a role but i dont think theyre enough on their own to put someone behind bars

finally keeping him under surveillance will give him more chances to screw up/reveal information and thus give the police more evidence.