I work on a contract for the CDC and we open sourced an older version of the software we display data on maps in: https://github.com/CDCgov/CDC-Maps
I'm working on switching our development to open so we use the same codebase that is available to everybody and adding other visualizations. It's slow going but there is movement there. I do agree it would be beneficial to fund open source projects, likely by including some requirement in contracts.
I think them funding projects directly with cash could cause a lot of problems though. The increase regulations that would need to be added would probably not be worth it for open source projects. People who get funding would likely need to submit a lot of documentation, there'd also probably be weird rules about non U.S. citizens etc... and laws would need to be passed.