What you are arguing against is a very common, and very wrong, way to explain how quantum computers work. It is notoriously hard to explain it concisely, but even Trudeau did better than that.
You do start by putting all the solutions of the problem in a superposition, but that in itself doesn't help, as if you just try to read it off you will get a random solution. And a random solution you could get just by running a classical computer with a random number generator.
What you have to do is make all the solutions interfere, a delicate coreography of wrong solutions cancelling each other and correct solutions being reinforced. After that you make a measurement, and get a correct solution with high probability.