Do not pay for a Ph.D. Especially do not pay for a Ph.D or MA in the humanities. Any program that’s worthwhile and wants you will provide full tuition and assistantship. Not offering you a full ride plus stipend, just means the program doesn’t really want you but is happy to take your money if they can get away with it.
Professional programs with a clear non-academic career path, e.g. law and medicine, are a different story.
The correct response to Hamming’s question is “Because I have a comparative advantage in working on the problem I am working on”. There are many, many important problems in the world of greater and lesser degrees of importance. There are many, many people working on them, even within one field. It does not make sense for everyone to attack the same most important problem, if indeed such a single problem could even be identified. There is a point of diminishing returns. 100 chemists working on the most important problem in chemistry are not going to advance chemistry as much as 10 chemists working on the most important problem, and 90 working on a variety of other, lesser problems.
This point was first made to me by Richard Stallman who told me quite clearly that free software was not the most important problem in the world—I think he cited overpopulation as an example of a more serious problem—but software freedom was the problem he was uniquely well situated to address.
There are seven billion people in the world. I know of no problem that actually needs 7 billion minds to solve it. We are pretty much all well advised to find the biggest problem we have a comparative advantage at, and work on solving that problem. We don’t all have to, indeed we shouldn’t, all work on the same thing.