WA seems like a generalization of that. Instead of seeing it as a google-killing AI inference engine, you're saying to think of it as a way to do effortlessly what you could do already... if you went to the trouble to gather the data, put it into mathematica or similar analysis tool.
This is a very credible claim, and I can imagine it quickly finding unforeseen uses, as you say - provided it really is reasonably effortless (as in your four criteria).
You can click on the first link - your answers are there.
Notice that the two examples you gave belong to a fairly narrow field - statistics, something that seems to be the trickiest to collect in more or less structured form. But try it yourself, you'll see how easy it is to find virtually anything nowadays. In most cases there's a good chance someone in the world thought about something you are interested in and has put it out on the Net already. If you are the first to ask a question, then I doubt WA will give you useful results either.
Will most people realize the sorts of questions they can ask? Probably not. Do most SQL datasets get used to their fullest potential? Probably not. Imagine what it does for the curious student, journalist, or professional, though.
Some things I'd like to see:
1. Percentage of population in African countries with HIV/AIDS over time. Regional, or demographically coded information would be interesting as well. I'd also like it sourced. I could go look this up somewhere... or I could just ask WA.
2. Fertility vs. per capita GDP for countries/regions in the world.
This is not to mention all the historical event, chemical, physical, etc. data.
Imagine NYT data visualizations built on WA data. Private data sets that people slice and dice with WA and then sell specific visualizations, etc.
It's a problem we don't know we have. Success will critically depend on flexibility, ease of use, and accurate and broad data sets.