You can't just cut these programs without irreparably damaging your political career, which most politicians aren't willing to do. Whenever cuts in Social Security are mentioned, the cry is raised that our elderly people are being robbed from. They paid into the program, and now they may not be able to withdraw. Ignored is that fact that these people are withdrawing far, far more than they ever paid in. It can only get worse, given today's emphasis on reducing world population and the shrinking work force.
Pregnant teens are an easy target, because they have obviously done something wrong.
They are also not regular voters, which makes them a more likely target than the elderly, who vote regularly. I deplore the moral standards which wink at and reward those who lack the self control to wait until an acceptable time, but I don't relish the thought of punishing them by starving their babies. Welfare is actually a name used to describe many different programs which all do roughly the same thing - give money to poor people. Some of them used to try to do more, but increasing government regulation and restrictions make it harder to do anything but give away money freely. Welfare fraud is rampant and examples of abuses are plentiful.