Actually, there are several reasons for attacking as DS. I'll give some examples, but there can be more
1. General principles for why it is good to attack, at least a little.
The LS is generally stronger on the attack, and the longer the game goes on the more opportunities the LS has to make that edge count, even if they just do one or two damage per turn, it still adds up. Also, many LS decks have cards and combinations that create "instant win" from an underdog position, a well timed yoda with trust your feelings and a lightsaber, a home one or red two with a leia, or just two rebel assaults. When you have a good defense, it can be worth attacking with one unit with a blast icon just to start putting a little pressure on. This is even more important if you use "the ultimate power" objective set (getting two clicks with a laser blast because you destroyed an objective already for one click is pretty nice). Also, remember that you always start the game at an odd number, 1. So even if you control the force all game, destroying one objective will shorten the game by one turn, which can be all the LS needs to win.
2. Destroy objectives key to the LS strategy
Often you can identify certain objectives that are just vital to the LS setup. Against hanjedi for example you usually want to try to destroy their Cantina or their last minute rescue, to prevent healing of those pesky guardians. You might want to destroy their "mobilize the squadrons" if you are playing against rebels, to make sure that they cant use that extremely powerful two resources per turn card. Other examples exist. Identify your enemies strategy, and strike a key objective to kill it and disrupt their plans.
The LS can often work wonders if left undisturbed to play the game they want to play. If you have a ds deck with tactics icons you might want to attack to tie down powerful units so that they cannot act in your opponents turn. If he attacked with home one, and you can attack to put two focus on it, it's a great way to save yourself some headache on the next ls turn. You can also make the opponent block with units committed to the force, focusing them twice and perhaps keeping them tied down and you securely in control of the force. In a deck with TIE attack squadron, a vader with lightsaber, or a boba fett with mando armor, attacking gives you the opportunity to "strike out" a target.
Just some thoughts.