It all depends on the privacy level of the profiles to be merged.
Merging a profile is like editing or changing the information of the profile.
If both of the profiles to be merged are "Open" any Wiki Genealogist can complete the merge after the approvals for merging the profiles are recorded. (Privacy "Open" - any WikiTree member in good standing with a confirmed e-mail address who has signed the Wiki Genealogist Honor Code can edit it).
Merges of profiles with privacy level other than "Open" need to be completed by someone on their Trusted List. If none of both profiles are "Open", only someone on the Trusted List of both profiles is able to complete such merge.