When I say that governments should contribute, I meant by spreading the word about free software, sharing training materials and issueing bug reports. Government does not need to write office software. It already exists. They should simply become part of the community. Because public funds should benefit public software, which builds the common good.
Government usually also order special software to be written for special tasks. There is a huge backlog of this kind of software in use, which makes any transition, be it from Windows to Linux or from Windows XP to more modern versions very difficult. They could require all vendors that create software for them to license it under the gpl.
When I mean public software, I am also thinking about the "standing on the shoulders of giants" model. Free software distributions as we know them today are made up of thousands of little parts. When you want to create something new, you can build upon a lot of already created building blocks. This reduces duplicated efforts. Similar to how human knowledge works. Once one guy figured out how a wheel works, everyone benefits. This adds to the public good. By modularizing software and sharing as much as possible, governments can add to the public good, because duplicated efforts are reduced. Since so much free software already exists, governments don't even need to take the lead, as you seem to suggest in your comment. They only need to participate.
> If government is going to push a scenario where it controls it's own software
The Italian military does not control LibreOffice, nor will they ever. They also don't control the Linux kernel or any other part of the Debian distribution. Or any other government. But they could require vendors that produce software for them to use as much free software buildings blocks as possible and modularize what they write and host those modules as independent open source projects, hoping that other government entities, possibly even from other countries, or simply other entities will make use of those modules. This strategy indeed reduces the control the vendor has over the product and thus "increases" the control the government has over the software. But only in as much as anyone else in the public now controls said software. Though, again, this only applies to special cases where governments order software to be written for them, which happens a lot more often than you might think. And it insures the government against a lot of problems, including, but not limited to bankcruptcy of the vendor. On a sidenote: There are as many reasons for open source projects to exist as there are open source projects out there, but I have heard a small company (two people) that said they were required by their client (a rather large company) to turn their software into an open source project to guard against issues stemming from buying from such a small company. So this very thing is already happening in the private industry.
Though, again, my main point is not government controlling software, but merely government participating in community software. Which brings us to an argument that I haven't mentioned: Where the money flows. For US government bodies, this doesn't apply as much. But this is Italy. When "buying" free software, government entities have the option of spending the money locally, as opposed to giving it to a US company. Which also is a political issue.
Last but not least: Those are all political arguments. I agree with you about costs and I respect your opinion. People have different opinions about politics. I simply explained mine.