Having consulted to scores of public sector projects, the institutions are artifacts of their incentives. See the Gervais Principle for example dynamics.

An internal GovCoin would technically work very well, as unincorporated project billings and budgets aren't real money inside large organizations. The main question is, for who? It would obviate layers of management in organizations whose main purpose is to generate layers of management. The only time real money gets exchanged is during settlement with outside vendors, otherwise, it's fiat funny money run through multiple inconsistent departmental ledgers.

Imagine it working inside a university, and then expand that to government ministries, as they're organized in essentially the same way. They don't want a means of exchange based on consumer need or desire, they want to decide based on narrative discussions.