Instead we are teaching them to remember stuff for long enough to pass that test/exam...
I absolutely agree. Unfortunately, we don't do enough to attract the best people to the profession, and we don't let them teach in the right way.
I'm a big believer in open-book testing as a far more realistic test of students' problem solving skills. People in the real world certainly don't memorize all the facts they'll ever need, so why expect that of students? (Believe me, good open-book tests are not easy. The hardest tests I've ever taken were open-book.)
Unfortunately, each open-book test can only be used once, so they're much more work for the teachers. That's why we have so many closed-book tests that are more about the students' ability to memorize and regurgitate facts than in actually applying them to problems.
A good education teaches not facts so much as methods -- especially how to use your references and design tools to solve problems that no one has solved before, with no answers to memorize or look up in the back of a book.
In the days when I taught, one of the things I used to tell students was that it wasn't necessary to know everything, it was just necessary to know how to find out. If you understood how to read and interpret technical resources, and knew where to find them, you would be fine.
I think all of us specialise in one way or another - it's the nature of the beast and we wouldn't have achieved what we have as a species in any field were it not for dogged persistence and 'satiable curiosity'. For some people it's the players of their football team and the results over the years, for others it's music, for others it's science.
I follow a blog where you can, erm, check out electronic books before you buy them *cough*. Some of the books are incredibly obscure, and it always amazes me that the tiniest speck of human interest will have been examined under the high powered microscope of human curiosity by someone somewhere.