Well, the issues/solutions you propose are a little extreme. But in most cases, the main reason is that politicians are afraid of ostracizing constituents. This is the main reason every politician (democrats and republicans) almost always spend more and rarely cut the budget. Cutting programs means angering some demographics, whereas adding them means pleasing more. By confronting an issue, you win the supporters over, but lose all of the opponents.
However, as mainstreet said, 13 year olds aren't really ready to make that decision as to whether they are ready to finish their education. What's more, requiring that attendance helps deter a class of uneducated folk who won't be able to find work and thus, become dependent on the government.