Firstly, "teaching the controversy" or "critical analysis of evolution" is literally teaching Intelligent Design.
There is no fully developed theory, as Philip E. Johnson has admitted:
"I also don’t think that there is really a theory of intelligent design at the present time to propose as a comparable alternative to the Darwinian theory, which is, whatever errors it might contain, a fully worked out scheme. There is no intelligent design theory that’s comparable. Working out a positive theory is the job of the scientific people that we have affiliated with the movement. Some of them are quite convinced that it’s doable, but that’s for them to prove…No product is ready for competition in the educational world."
ID really only consists of a series of arguments against evolution, the default conclusion of which is a designer. Teaching the controversy allows all of these arguments to be aired. Only the designer's identity is left out, but it's pretty darn obvious.
The world won't fall apart if a generation of people, and even scientists, dismiss or never learn evolution. Even in cases like flu vaccine updates, doctors would keep doing what they're doing because it works. They'd just come up with different reasons why it does, as in, "God works it like this." Nothing supports a theory like evidence which the theory itself was changed to match.
The true consequence is that we would lose our insight. We can apply proven techniques and technologies and rationalise however we want, but if we don't understand the true reasons why they work then we can't refine them or make any new ones except by trial and error. We stagnate.
As Ken Miller has suggested, a country which sacrifices scientific understanding to maintain its beliefs falls behind the rest of the world. He's terrified that this will happen to America. I worry too, but I do think some hard data showing the country's slipping technological superiority would spur some patriots to give science a shot in the arm. I hope it isn't needed of course. Anyway, I'm Australian.