Amazon's Alexa subsidiary once offered a service much like you describe, called "Alexa Web Search". But: "The Alexa Web Search web service has been deprecated and is no longer available for new subscriptions." [1] Also, I think (but am not sure) the Alexa Web Information Service originally offered hosted read access to the full content of Alexa's recent crawls, but it no longer does. [2]

It also seemed like Amazon was building up web-scale search expertise in A9, but the only apparent results are work in metasearch/aggregation. (They already have a technology called 'OpenSearch' [3], so might have a hard time repurposing that name for something else.)

So it's almost as if Amazon was deeply considering your proposed strategy, then backed away.

[1] http://aws.amazon.com/alexawebsearch/

[2] http://aws.amazon.com/awis/

[3] http://a9.com/-/company/opensearch.jsp