Science is reproducible regardless of the availability of the source code. I speak as someone who has been busily reproducing results without access to the source code since starting my PhD. :)

I think making code available could be useful, but in a world where your worth as a scientist and your job security depends on getting published and getting cited, there's a conflict of interest that is incredibly hard to resolve. What really needs to happen is some sort of method of measuring the impact of released code as well as the impact of released papers.