Why would they run their own Usenet archive? Google had the Usenet archiving business sewn up, and by the time they started showing signs of being untrustworthy it was too late and much of the 80s and early 90s stuff only exists in their archives. (Oh, and as a side note apparently a lot of the interesting porn from that era has been lost to history too.)
Trusting any one service to be the bearer of internet history carries the same risk, that the service can go down at any time, and take its data with it. If this information is to be preserved it has to be hosted somewhere, preferably multiple places. If it's to be accessible online, then someone has to pay for the servers and the power and the maintenance.
Google's an ad company, they don't have an obligation to be the arbiters of human history, whatever their slogans might be regarding 'organizing the world's information'. They care about the information that makes them money.
