you are totally right! You have spotted the emperor's new clothes.
Many, if not most, cases can be solved with common sense and some very basic business concepts (profit and loss, break even, distinguishing fixed and variable costs.)
I would daresay that 99% of consulting problems are of that nature as well. Very rarely you will encounter a problem as you do in physics, engineering, math etc. where you just don't know whether there is a solution to a given problem or even don't have an idea how to get there.
Consultants, despite all the business hokey-pokey, power suits, and buzzword bingo, still only cook with water and often times pretty lukewarm water at that.
So yes, if you have your wits together, don't crack under pressure, and have some basic business concepts handy, you can absolutely nail 95% of cases.
That being said, structureis a whole different animal. I have encountered very few business people without a consulting background that were brilliant at structuring. I am convinced that a good part of the money we as consultants are paid is actually for this: The ability to break down a problem and structure the path to a solution and present it in a structured manner.
So if you are confident that you can solve the problem, just work on the structure part.