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Even with a hosting service, there might be hundreds or thousands of sites (and differing contexts), run by different people, on a server. There might be many servers in such a company.
It's also extremely likely that they don't have the technological capability to spy on people (or it would involve the use of considerable resources), as that would greatly constrain possible technologies that customers could make use of, and undermine their security.
Also, spying on random things on a server is clearly bad for privacy. Do you want your trade secrets to be siphoned off by someone's half-baked algorithm? Have you begun to think about how stupid this idea is?
