Am I missing a limitation on double strike (for star wars lcg)?
The engagement isn't over until all ready units have been focused to strike.  Double Strike must be played "after a Character unit is focused to strike," which means it can only be played, and therefore can only remove a focus token, DURING the engagement, allowing multiple strikes at the same objective. If you can destroy an undefended objective in one strike, playing Double Strike does nothing for you- your second strike has nothing to hit.
See "Resolving a strike" on p 20 of the rules, and "Engagment resolution" (p 31).   CArdgamedb.com is the best place for Star Wars rules and discussion. Some real experts post over there.  Check it out!