Are missing person homicides less likely to be solved due to 48 hour rule?

I have a friend who has an elderly family member who is missing under very suspicious circumstances. Though they took a basic report the police did not begin an active investigation until after 72 hours missing.

Please note that this question is NOT about bashing police procedure. I realize why they delay- most missing people return home and are not endangered.

According to statistics the most crucial time for a homicide to be solved is within the first 48 hours. The chance of solving a case is cut in half if they don’t get a lead within the first 48 hours.

I am just curious to know if delaying an missing person investigation that is later found to be a homicide reduces the chances of catching the killer by 50%?