Don't you think that they would have tried that if it was an option?

For academics, it's a global market for talent. There may only be a small number of people in the world who are doing top research in a particular area.

For rural healthcare, if you're a hospital in a very poor, very remote area, and you want to hire say, an anesthesiologist, you have to hire someone who could make very good money working anywhere, but is willing to work at your hospital. $10k is not going to cut it.

No, because the existence of an underclass means it will be used. See agricultural labor and how an underclass prevents mechanization or wage increases.

Luckily, administrators' salaries and endowments can cover fees, and rural areas are often served by doctors who agree to loan forgiveness programs which help underserved areas.