I would like to throw in the often used "Public Money = Public Code". I personally agree with your sentiment but would like to throw in that an open source, but not open contribution, similiar to SQLite may be a good addition for using OSS at this level.
Largely licensing issues. For example, from SQLite's copyright page [1]:
> In order to keep SQLite in the public domain and ensure that the code does not become contaminated with proprietary or licensed content, the project does not accept patches from people who have not submitted an affidavit dedicating their contribution into the public domain.
That's not any different from the many open source projects that require a CLA.
Also, SQLite would have it easier if they had chosen, or written, an actual open source license rather than a public domain dedication considered invalid in many countries; they even sell "yes this was meant to be open source" warranties.
While 1. may be meaningful on mainstream IT FOSS projects, this has probably next to 0 relevance to gov FOSS services. Issue 2 is solved already. Issue 3. also seem irrelevant - I doubt folks other from academia and specific nerds will try to PR on gov service given the extensive in domain hard to get knowledge that is needed for that in genral.