I think you're over-representing just how well opinion surveys can represent the actual will of the people.
To put this in a less politicized analogy, everyone will tell you they want to be rich, but how many people are willing to make sacrifices to become rich? It turns out many rich people today are rich because they didn't have to make very many sacrifices, while most everyone, including minimum wage employees, can become a millionaire. Mathematically it's not all that complex.
People will tell you what they want with some internalized model that isn't representative of the realistic trade-offs that would have to be made. So in effect what people say isn't based in the reality of what they actually want.
To put this in a less politicized analogy, everyone will tell you they want to be rich, but how many people are willing to make sacrifices to become rich? It turns out many rich people today are rich because they didn't have to make very many sacrifices, while most everyone, including minimum wage employees, can become a millionaire. Mathematically it's not all that complex.
People will tell you what they want with some internalized model that isn't representative of the realistic trade-offs that would have to be made. So in effect what people say isn't based in the reality of what they actually want.