Except I wonder are they ? Now there is specialism for the roles of referee and AR I think a good case could be made for saying that the persons with the flags are not referees but following a different craft. If a referee goes down injured it isn't one of the ARs who steps into the role but the 4th Official. So, if anything they are Referee's Assistants but much better to be given their own style, title and dignity of Linos or Linespersons.
At the top level, I would agree with you that their role is a "lining" specialism.
At most levels of the game (where the players are fortunate enough to have three match officials), the senior AR would take over in case of need.
Maybe we should call the specialists: Professional Linos and the remainder Assistant Referees. Better suggested titles for the specialists welcomed!