And I've worked at a long series of companies that don't. That's the thing: different strokes for different folks, as it were.
Maybe I'm unusually hardcore?
I think it's less about degree-of-core-ness and more about platform and domain knowledge. Personally, if I were hiring for what I consider to be a fairly typical company, I would be looking mostly for ability to consistently get functional, bug-free code running. I would likely seek stronger algorithmic knowledge in some small ratio of employees.
I guess I feel strongly about this because I think it's fundamentally disrespectful to all coders, and ignores the tremendous variety of tasks and skills out there. A self-taught hacker who can get a great product going in a short time may be just as important and valuable to a company as the algorithm-strong coder who catches scaling problems before they come up. When it comes down to it, the goal is to create product and value, and that happens in many, many different ways.
The fix will even look very simple. The insight going into the fix isn't as simple, though.
That's true of the majority of bugs I've written or come across, whether its related to performance, crashing, or unpredictable behavior. In fact, looking at fixes that coworkers make to your own code can be a tremendously enlightening (and humbling) experience.
Then I would hope they have a good sense of usability, if they are writing user facing code. And I would hope they have a good sense of algorithms and other aspects of scalability, if they are writing server side or systems code.
Maybe I'm unusually hardcore? I'm definitely not all about the algorithms, but I work on a lot of systems programming.
The other thing is that often you don't realize that what you're doing requires thinking of this until somebody else has to go fix what you wrote. The fix will even look very simple. The insight going into the fix isn't as simple, though.