[dragonwriter]

> Why is the solution that the nation just foots the bill to make a bad investment instead of the individual?

Almost the only economic reason in a rational choice model [0] for a public program is the existence of externalities that justify action that would not occur in a market system without government intervention to internalize the externalities; in this case, that would be diffuse social benefit that offsets the negative expected financial return to the student if they paid full price in the market.

Of course assessing the existence and, particularly, value of such externalities is, in practice highly subjective.

[0] which is known to be inaccurate, and real-world irrationality may provide additional reasons.