The advantage lies more in a higher rate of activated muscle fibers within the targeted muscle than the number of supporting muscles involved. AFAIK there's no consensus yet why this is, but I think that balancing play an important role. Especially dumbell exercises have a high EMG score. For example decline dumbell presses has the highest EMG score compared with other chest exercises with barbells, machines, cables and from other angles.
Officially your core means your whole body minus your legs and arms. You're correct that every muscle functions as a stabilizer, but in case of your core it's more about muscles who play a more active role in this process, like the lower and mid section from your back & abs to keep your torso in position, your neck for your head, hips for your legs & torso and delts for arms & torso. There are specific exercises for those areas but it's also important to let them work together. Imagine yourself in a wheelchair for a year with two daily options for 1 hour: 1. isolation exercises or 2. walking. I would definitely going for 2 because walking would be tough after 1 year with only the option #1.
Because most of us use those muscles to less because of modern times. We sit, we drive, take the lift, etc. For example strong abs help to prevent lowerback pain.
See my first reply in this post. A contraction is only a contraction on fiber level (activated or not).
The more muscles and balancing work is involved the harder it gets to perform them. I always tell impatient clients that they first need to control the movement & weight before going heavy. Of course this is nothing less than logic, but this is just beginners experience.
What activates the fibers is the load presented on them. Light load, less activation. More load, more activation. This is different from muscular inroads where the load is relatively light but repetitions high.
If you want to get good at walking -- walk. If you want to get good at managing a wheel chair -- roll around on that chair. Neither will help the other.
The body is very activity specific. This started to dawn on me when I rolled around with a Jiu-Jitsu novice who was a top notched marathon runner. Now when I say rolled around I had no intention of smashing him but just roll and let him practice on me. Is main problem was he just kept getting winded. He couldn't keep up with me conditioning wise on the mat. But I assure you I couldn't jog 10 miles let alone keep up with him in a marathon.
A lot of the conditioning training that coaches have their MMA fighters do: moving tires, chopping wood, pulling sleds, jumping around, even low intensity jogging, will do little or nothing in increasing a fighter's conditioning for a fight. Dan Gable was once asked what was the best exercise to be in shape for wrestling. He said "Wrestle."
When Joe Stevenson fought B.J. Penn of course he got smashed but he was barely winded even though B.J. was huffing and puffing. And Joe was in all the bad positions that exhaust you -- being on the bottom. His training consisted primary of very activity specific drills. Actually rolling and fighting round after after round.
Did you watch any of the last TUF? Those big guys did all those state of the art conditioning drills but when they actually step into the cage they could barely get through the first round. They were in great shape. In shape for jogging, lifting weights, climbing rope, pulling sleds, but not for fighting. In their training they seemed to do little all out sparring and wrestling and it showed.