Be careful with that, because you are attempting to invert the problem. Giving Google Government approval to modify and remove content from views is the complaint.
While the initial discussion is always something small, it never ever ends up that way. The US did not become corrupt and full of cronies in a flash, it was incrementally done. So this time they want to remove content from ISIS. What happens when they want to remove content from "Tea Party", or an organization you may agree with? You should probably take a look at who the Government claims are the biggest threats. Like people who believe in the Constitution and individual rights, people who believe in the freedom of speech, people who believe in the second amendment, and people who question Government authority are all on the list.
Should the Encyclopedia Britannica have been able to remove content they didn't agree with to rewrite history as they saw fit? Sure, but there were other encyclopedias people would buy if that happened. If the same company was allowed to monopolize the market, would you still believe that they should be able to edit history as they see fit?
With the regulated monopolies we have, we lack that same freedom of choice and power of economic influence. Either freedom trumps and we remove regulations and government support which give companies legal monopolization, or we maintain our current status quo and allow the Government to control markets. If we continue the latter, we can't claim that these companies are private so get all the benefits of being private.