The simplest is "search for doc that contaons" . But we're used to "search for document about concept" by now. ISTRC Bing called themselves a "decision engine".

I don't know what Google is/trying to be now, but it often thinks it knows my business better than myself, excluding critical words.

I don't think there can be a universal answer. The corpus gathering is a huge barrier to entry, but having a common corpus would still allow room for competition on diversity of querying methods.