Some other research has shown that, in fact, if you do open up the solution process you can get anywhere from 10X to 100X improvement in problem-solving performance.
-- Karim Lakhani, Harvard Professor
Last-resorts will always look this way. Another way of stating this is that "An unusual solution is more likely to work than a standard solution that has already failed." Richard Feynman had a nice anecdote about this (which I can't seem to find on Google): his incredible toolkit of analytical techniques included a slightly obscure calculus technique (something about inverting and then integrating -- don't ask me for details). When his colleagues had tried all the standard techniques, they'd come to him -- and, pretty frequently, his trick worked. This gave him a great reputation, but only because they didn't know that he would have tried everything they thought of, first.
To really judge an unusual method (like open-sourcing a problem, or Feynman's math trick), you'd have to ask what happens when people try it first. And the obvious result would be: that problem-solving methods tend to be used in about the order of their utility, except in a few non-sound-byteable cases.