Ah, I see how what I wrote before didn't clearly express what I was thinking, and didn't address the issue of private contractors intentionally pushing for bloated contracts.
If public money for public code is mandated at the federal level, then private contractors would be bidding for work that ends up in the public domain. I am assuming that wasteful & bloated contracts will be underbid by contracts that fork or add features to existing projects. Either way, if the end result is in the public domain, then the project is still reusable.
I definitely don't believe that such a mandate would be easy to implement, or separate from a wider policy platform. I see private capital influencing government decisions as the crux of the problem with passing such a mandate. However, private capital influencing government decisions is an issue that unites many activists, organizations, and social movements. If FLOSS can be integrated into organizations and social movements pushing for institutional reform, then that might be a viable pathway toward meaningful policy change.