German state moving 30,000 PCs to Linux and LibreOffice - The Document Foundation Blog

That’s still not how governments work

It would be nice if it worked like that, but we both know it doesn't

That's called a pareto optimum

In reality it's gonna be something like:

M$ charges 5M €. Libreoffice might be 1M € so they will give 1M € to OSS and waste the remaining 3M € on some overly expensive one-time crap like car infrastructure. Later they will realize that they had understaffed their IT department and will need extra 5M € paid by more state debt.

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.