I happen to be one of those ski instructors you noticed on thinner skis.
One benefit of fatter skis is that they will enhance your tendency to keep your feet apart in turns. I had to relearn the sport, being older and accustomed to the collapsed knee comma type position. My race skis were enablers (in a bad sense). A fat ski forced me into more independent foot/knee motion and helped me to recognize the importance of edging on my uphill ski in the initiation phase of my turn.
I have two "fatties", both of which are in the low 80's under foot. I use quotes around "fatty" because by today's standards, they are not even considered "mid fat". I personally find the need to go no fatter than this, even when the powder gets very deep.
It is easier to change edges when the distance under foot is less. On my race skis (66 to 68 under foot), I can subtly switch from one edge to the other with only the slightest change of balance. Hence, in a tight mogul field, I can easily make two direction changes when fat ski skiers are committed to one. I can ski a tighter line closer to the fall line (if all goes well).
The problem is that my racing skis are stiffer and they tend to throw me more forward or backward in the bumps. The narrower underfoot dimension requires that a ski be slightly stiffer in order for it to ski smoothly. I find that I can make the fore and aft adjustments in order to compensate for the thrill of being able to change directions on a dime. In fact, if you watch a good skier on race skis on the flat you will notice subtle fore and aft balance changes indicating that he or she is "working" the fore section of the ski in the initiation phase and the aft end in the finish phase of a turn. Such motion has elegance.
My "fatties", although ever so slightly slower for edge change, tend to absorb the troughs of the bumps because they are softer. Also, these skis, although the overall snow contact area (which would be measured in square centimeters) is greater than race skis, are quite a bit lighter than race skis. This is, as Martha Stewart would say, "A good thing".
What was at one time a concern for me was that I assumed some of these fatter skis, because they were lighter, would be "squirrely" or dangerous to ski at high velocity on ice. I have been pleasantly surprised by the Volkl AC 40, the Atomic Stomp, and the Stockli Sormrider AT. All are roughly 184 in length. None of them misbehaved radically at 40 plus MPH - no significant chatter. I'd prefer to be on a race ski. But they did OK.
As for powder ... anything over, say 15 inches. I'd prefer to put the race skis away. But, even when conditions are bottomless, I do not find it necessary to go more than 80 under foot. I also find it inessential to mess with reverse camber ... at least until I own my own helicopter.
What is worthwhile remembering in the snow starved 21st century is that the vast majority of our inbounds as well as out of bounds skiing today occurs on firm snow. Deep powder is highly ephemeral. Arrange your ski quiver accordingly.