It is usually thought that to control the ball you need to slow down your game.
That is, if you lack topspin.
With topspin, you can exert your power without any doubts of your shot landing on the court.
You may hit some balls short, but they are still uncomfortable for your opponent due to the spin.
It is also thought that extension towards makes the ball go deeper, but that is not quite efficient.
Extension towards the target becomes more of a slap that a controlled hit.
First of all, the ball comes out of your racquet with less rotation or none.
Secondly, the arm is not connected as much to the body as when you hit across.
Power depends on two things: acceleration and weight applied.
Bending the arm connects the body to the impact much more efficiently, through contraction of big muscles, that following the ball with your stroke.
Additionally, it is easier to contract the biceps, quite a large muscle, that the fragile, small muscles of your shoulder.
Look at little kids attempting to put power on their strokes. They hit up and across, rather than forward.
Unless, of course, they have been trained at baseball, and play tennis forward with little control.
Apply the same principles to the two-handed backhand. Hit up and across.