Google is a monopoly on search. You could block it from indexing and it would drastically hurt you and your discoverability. Cutting your hand to spite you kind of thing. The same way you could in theory just not get telephone service or just not buy oil in historic US anti-trust actions. Media sites can't live of the little that trickles to them, and can't live without it either, with some exceptions ( like expensive paywalled editions like Financial Times). Thanking most news sources to piss off Murdoch and stop his crap from spreading might be worth it, for a few days but would be disastrous long term.