I am glad that someone else shares the idea that it should be possible to set tags manually.

Here is a list of API actions which need to be able to set tags:

• action=wbcreateclaim
• action=wbcreateredirect
• action=wbeditentity
• action=wblinktitles
• action=wbmergeitems
• action=wbremoveclaims
• action=wbremovequalifiers
• action=wbremovereferences
• action=wbsetaliases
• action=wbsetclaim
• action=wbsetclaimvalue
• action=wbsetdescription
• action=wbsetlabel
• action=wbsetqualifier
• action=wbsetreference
• action=wbsetsitelink

Makes sense to me.
Do other modules outside Wikibase already allow it?

See the linked task.