The counter attack has many objectives but the three main are: 1) It tires the other team out; 2) It gets you to the offense more quickly (giving you more time to attack); 3) It sets up mismatches or man up situations that lead to a higher percentage shot.
The more you can train athletes to be comfortable swimming (understand that countering is different than swimming: during the counter a player will stop, change directions, go from horizontal to vertical,etc) and stopping with a ball (and making passes then moving forward) the better off they will be in a game. This is a great time to get conditioning in as well.
A common misconception is that a great swimmer makes a great counter player. Additional skills are needed to excel as a counter player including ability to anticipate, ability to change speed during the counter and being able to absorb and dish contact.
Tony remembers at Stanford that the team rarely swam under Dante Dettamante because they would spend all practice doing counter attack. More fun and maybe harder.