The stabilizers used during free weight movements amount to nothing more than extra calories burned (and not many). The extra energy used by the stabilizers is energy that could be better used by the muscles being trained. The stabilizers are not receiving enough stimulation to cause growth so sometimes it isn't worth using them. Just my 2 cents.
I wouldn't go as far as to say that...
Stabilizing muscles contract to balance the body in respect to the lift you're performing. To perform certain lifts, to allow the targeted muscles to perform the lift, certain muscles have to contract to balance the body, to allow it perform the lift. Though these stabilizing muscles don't go through a full range of motion, which is generally the point, they do contract isometrically. These muscles aren't directly involved in lifting the weight, but they do stabilize the body. Sometimes the muscles that are used to stabilize a certain lift, might be muscles you are going to work on the next day. These muscles might be muscles you never actually work directly, but they are still important nonetheless.
There are good reasons why you'd want the body to have to stabilize the weight. First of all, muscles used for stabilizing the body during a certain lift do receive enough stimulating for muscle growth. Why do people advocate the use of squats and deadlifts so much? It's because lifts such as these require the body to stabilize itself (to the maximum), calling in numerous muscle groups to help stabilize the body. The squat and deadlift are strongly recommended in your program if you're trying to gain maximum strength and mass because the lifts themselves require numerous muscle groups to work to their maximum effort, and many more muscles are forced to isometrically contract to help stabilize the body to perform the lift.
Also, you want to strengthen your stabilizing muscles because without strong stabilizing muscles, you won't be able to lift as much weight in your regular lifts. This even goes outside the gym, concerning functional strength. Machines force your muscles to have to work against a resistance along a certain path. The muscles are set into a certain angle, therefore the movements are always super strict. Now although sometimes this can be used to your advantage, for the most part, it goes against what your main goal should be; to strengthen and develop your muscles from as many angles as possible, so that you activate and stimulate the maximum amount of muscle fibers. So when you work outside this range that you've been accustomed to resisting, you strength will drastically reduced, since your muscles won't be accustomed to that movement. So though you might be strong on certain machines, along certain set paths, you might find lifting a couch more difficult that it should be. This idea remains as the gym as well. If you tried to do certain lifts, such as a squat, a pressing movement, or a deadlift, and you haven't trained your stabilizing muscles, then you're not going to be able to lift a large amount of weight, i can promise you that.
So stabilizing muscles are more important to us than we usually give them credit for. I'm sure there are other good reasons why you'd want to have strong, developed stabilizing muscles. I can't imagine being able to achieve your maximum developmental potential without full working every muscle group to the fullest.