I think it would be nice if Strategist could have some battle "perk" (e.g. Scout has Vault adv., Salvager has relic gain, etc.) As it stands now, Strategist, while important as a capacity, is rather useless as a role. Basically this means that while it's important to draft a Strategist, there's no advantage to having that player in the Strategist position. Thus, when drafting a Strategist who is also a good player (which is true in most cases IMO), it's advantageous to leave the position for your "worst" player. Some Generals/Lieutenants are probably capable of adequately performing this position as well, making the Strategist position even more "useless"
Not sure what kind of perk would be good for Strategist. Possibly something that affects discard/salvage, or maybe some sort of lasting effect on the opponent (e.g. Strategist salvages 3 more cards or discards 3 less, or Strategist chooses which cards the opponent discards on a win [or even what they salvage]).