[miscfuck]

On a hash with a million elements, the O(n) hashing of a 10-char key is negligible.

Also, you have to make apples to apples comparisons. In this case, you're comparing the time to search against the number of elements, and that's it. If you want the time to hash AND search - as a function of n - then your analysis holds, but you can't then compare that against other datastructures that do not have an equivalent hash step.