That, again, is not how governments work.
What you depict is how companies work: You save amount X on something, so there are X moneys left to invest in something.
Governments work with separated and highly regulated budgets. That is sometimes bullshit, but sometimes necessary to make sure government aids are spent fairly, for example. So: You save amount X on something, you aren't allowed to just give this amount to someone. There has to be either a program, a law, or (most often) an entirely different budget somewhere else that this someone is allowed to receive.

So the “trade-off” logic cannot be fulfilled by governments, and it shouldn't be. Think about the myriad of bullshit, money would just be dumped into by the government if this wasn't the case. On top of the myriad of bullshit that already made it through the nets, that is.