It seems to me that fewer people may want to contribute to the effort if they think their freely-contributed work could be subsumed by a patent fence that (e.g.) GlaxoSmithKline might decide to slap around a derivative discovery.
In practice, you are almost certainly incorrect. Scientists working in basic research - the ones I've met, anyway - are almost universally thrilled if their research leads to improvements in human health, regardless of whether or not they or someone else profits from it. (In fact, I was unhappy working as a developer on an academic project that was partly funded by charging companies for access to our software - I thought we should just give it away, because I wanted as many people as possible to use my work.) I have no fondness for GSK or any other big pharma company - quite frankly, they're a pain in the ass to deal with - but the extent to which they leech off public discoveries is vastly overstated, and they perform a huge amount of very expensive and very boring work to bring drugs to market. This combination of publicly-funded basic research and privately-funded development is one of the primary justifications for the existence of the NIH and on the whole it works relatively smoothly, although the perverse incentives of the Bayh-Dole act are problematic.