You first look into the direction the cara are coming from (left in your case) and wait until you can cross the road. Then you check the other side just in case and while crossing the street, you look in the direction the cars are coming from again just in case something crazy happens.

If you look right first and then left, there night be cars coming from the left in which case you’d have to wait until they pass, then look right and then left while crossing the road. So your proposal would lead to one extra “looking to the side” if there happened to be a car coming.