I like the idea of having a government department have to defend their budget or explain why they exist. However, your point reveals a fundamental flaw in government budgets supported by tax income. Even if they are fiducially responsible, they are restricted from doing so. Here's how:
Government budgets and programs demonstrate their existence by showing how much money they spend. If they don't spend the money, they won't get funded next year. This disincentivizes prudent spending, rainy day funds, etc. If they are too careful with the money at the beginning of the year and have leftover cash, they hurry up and blow it on stupid shit so they can continue receiving funds.
As you know, business works the opposite way, and to your point, companies survive on prudent spending, management, R&D, paying down debt, acquisitions, etc.