The real reason government prizes won't work is that there is no place for the vast army of NASA scientists and employees in an organization whose job is simply to hand out prizes.

I disagree with your reasoning on prices. Having someone come up with a $1 billion idea to get to Mars to win a prize of $50 billion is a solid bargain, especially when you consider that the government would certainly spend at least $100 billion to get the same job done. And when you throw in the fact that now we apparently have a space technology cheap enough to allow you to get to Mars for $1 billion, the entire solar system opens up to commerce and exploration. Even more of a bargain.

Throw in the fact that you have just given a red-hot space company $49 billion to play with, and the sky is the limit.

In real life, of course, the numbers would not be nearly that widely spread, unless there is some major physics breakthrough just waiting in the wings. And a prize for a trip to Mars is overkill. Frankly, prizes are a lot more realistic for things like putting people in orbit cheaply or something along those lines.