when i was unemployed and toyed with the idea of foraying into the world of personal training, i downloaded and read through the NASM (national association of sports medicine) training manual, just to see what their take on everything was.
their main argument for instability training is that it increases proprioception and makes the body more "functional".
i think the real reason is that it helps trainers possess a greater wealth of special expertise (i.e. knowledge of 'exercises') without having to learn the biomechanics of the more basic compound movements. also, while the compound movements may have a stigma of making you 'bulky' or a 'meathead', all that instability bullshit plays into the 'high reps for toning' misconception.
in a first session, a trainer can come up with some ridiculous 'core and stability' exercises, which will be difficult for the client, even with a light weight. then the trainer, who at a commercial gym is generally a beginner in their own training, can demonstrate flawless 'form' in the kneeling swiss ball curl, or any other balancing act.
the most unstable i'll get is bulgarian split squats or db bench on a ball, otherwise, i'll get my proprioception from squats, deads, olympic lifts and pressing