I agree. However, I find this approach very rare. The current trend it that every erudite should read Hemingway, Nabokov, Catch 22, and many other books. I think it is worth time for some people, but not for the whole society.
My approach, shortly speaking, was that I've found most of the stuff not challenging at all. So, I raised the bar, reading literature critique. Then, I realized it is pure bullshit, and jumped into sociology, then into philosophy, then into philosophy of mathematics and it turned out that pure textbooks are much more interesting after all.
Shortly, I agree it depends on the goal. Keep in mind, though, that people's goals vary a lot. And that's my point rephrased otherwise: if you are not interested in reading something, give up. Unfortunately, the current trend is to read books, and if you find nothing in them, the problem is in you. I try to fight with this symbolic violence, whenever possible.
@klipt, I don't want to create so many responses so I will give you the feedback here.
Yes, I read all the books you've mentioned, except Pratchett, which bores me to hell. I've found Goedel's proof itself more enjoyable to understand than the books about it. The commentaries, in this particular case, seemed mostly unnecessary. (I don't like this fetish of Goedel's work that extrapolates its misunderstanding to all other ares; eg, Putnam)