I believe that this kind of thinking is what differentiates the companies that are successful in the long run from the ones who can create a one shot product; and I'm not sure the OP is on the right camp.
To take an internet-famous example, Kevin Rose went on the record to say that one of the major failings at Digg was the fact that they hired anyone who could code in PHP in the beginning, but when a PHP-based solution stopped being the answer, they were left over with a bunch of PHP developers who couldn't do anything but that.
If your mexican restaurant finds out that the most successful part of the business becomes making dessert (Mexican at first, but then onto other kinds of styles), then they would be happy to have picked someone who can actually cook something else than just Mexican food.
I think the whiteboard tests are an attempt at figuring out the capacity of the interviewee to abstract the problem instead of solving it the fastest/usual way. In my experience, the ability to abstract is very closely correlated to the ability to adapt to new situations (and code better in general)