Lois, to answer your question, there is no specified protocol for who should do the merge. Theoretically, the PMs of the profile should take care of it within the first 30 days. But if they don't, once the profiles have gone to default approval anyone can do it, PM or proposer or whoever, without reservation.
As a matter of courtesy, as a project leader, if a project-managed profile is proposed for a merge, I usually wait for the other PMs (if any) to approve and complete the merge. If it doesn't happen by the time it goes to the 30-day default approval, then I'll complete it.