One of the early sales pitches for Avalon Hill wargames is that YOU are in command, as shown by the box art for Tactics II, above.
Generally I like games where you can identify with some historical personage, but lots of times this is impractical. For example, in a two-player game of Napoleon or Waterloo, the allied player will be portraying at least two individuals -- Wellington and Blucher.
In many games it's even harder to pin the player as representing some distinct individual and the player really represents a corporate body. Players often make decisions at several command levels, for example. If you're playing Chickamauga you're obviously the army commander, but you are also determining the deployment of individual brigades, which the division commanders would do.
The odd thing is that many games that tout their realism are some of the most unrealistic in the amount of control they give players. In ASL, for example, players who must represent battalion commanders are also driving tanks hex-by-hex down a road and rotating a turret -- and selecting the ammo to fire.
This is one reason I'm tending to appreciate games like Memoir '44 or Tide of Iron more, because their limits on player control seem more realistic to me.