Should not that money go to the State?

Why should the money automatically go to the state?

It should probably not go to the claimant because this would encourage spurious lawsuits for the sole purpose of trying to gather lots of money. Assuming a non-corrupt government, it should go to the state (or other level of government) so that it could benefit everybody, e.g. via tax breaks, or more investment in science, medicine, education, etc.

In practice governments are corrupt, so the answer is a bit more complicated. If the money does go to the government, how do we make sure the government isn't tempted to cause the punishment to become unfairly severe in order to gather more income?