Edit: they do fund a lot of PhD research in US universities, including fellowship for PhD students. But one can't expect a company, even Google, to overhaul the entire system
As it stands, US education is all over the place, and worse, it's more and more only becoming available to the elite; social mobility is low, that is, if you're born poor chances are you'll end up poor yourself.
This is unlike where I came from, where my dad was a low paid metalworker but I got an effectively free college education and repaid that government funding multiple times over in income taxes in just a few years, whilst simultaneously bringing a lot more money home than my parents did (to oppose any "but income taxes screw with my income" claims).
Anyway, since the government isn't doing it, I do think it's up to the big companies to offer it. That's what the US is all about, isn't it? Changing it to a capitalist government, where it's big companies that rule the people, not the government.
It is for this reason that I don't think private companies can significantly change that, even in the US. Even the most innovative/successful companies don't last that long in the US to make a significant change in the Education system.
And to an even larger extent it's up to the citizens of the U.S. Most don't care enough to support/reward such efforts at the ballot booth, so the politicians aren't motivated, and things don't get done.
Unfortunately, when it comes to legislation and budget considerations (including education), lobbying works.