"rely on Wolfram Alpha to either give you the right answer (depending, of course, on the accuracy of its own index), or no answer at all."

This is wrong because of weaknesses in query parsing/explaining. I tried out Archimedes's sand-reckoner problem (how many grains of sand it takes to fill the solar system); it rephrased my query as "planets volume / volume of a small grain of sand" (which sounds reasonable) and gave an answer off by 17 orders of magnitude, taking "planets volume" to be the volume of the median-sized planet among all the planets. Its query explanation didn't link to any explanation of "planets volume", so I had to make that a separate query to find that out.

They could solve this problem with a better interface to its understanding of your query.