That wouldn't stop people from doing it privately. For example, biochemist Peter Mitchell (https://secure.wikimedia.org/wikipedia/en/wiki/Peter_D._Mitc...) won a Nobel in Chemistry in 1978 for work he did entirely without government funding, out of a house he owned. (It's not some little thing he discovered, either - if you take an undergraduate course in biochemistry, you'll run across his chemiosmotic hypothesis directly, and it's taught in less detail in a lot of other biology courses.)
But both cases are probably marginal. In a world where one has to earn money to survive, innovation is slowed down, either because of copyright and patents, or the lack of funding.
The trick is to get a world where one doesn't need to earn money.
At the very least we need to move towards a place where money is not the final arbiter of 'Good'.
"Intellectual property rights has very little to do with individual initiative. I mean, Einstein didn't have any intellectual property rights on relativity theory. Science and innovation is carried out by people that are interested in it. That's the way science works. There's an effort in very recent years to commercialize it, like they commercialize everything else. "
(If that description of corporate productization sounds unfair, I think it's closer to the mark than saying basic research is analogous to "someone banged out a prototype over the weekend".)
When it's able to be productized, that's when corporations come along. This is well known. (http://www.nytimes.com/2005/04/02/technology/02darpa.html)