>None of the code is open source
Well, not all, for example mObywatel was recently open-sourced (in a ridiculous way, but still).
I think you raise some important points. In my opinion, a lot of code funded by public money should be open-sourced, but it's not as clear-cut as some people believe. I'll use this comment to point out some of fallacies that people responding to you make:
>Also open source government code means other governments can fork it, overall lowering implementation costs, while still keeping code sovereignty.
This is completely unrelated. French government won't deploy a Polish public health management website just because they found it on Github. For projects of such magnitude you need deep mutual cooperation between both governments, and a lot of changes. Making the code open-source is the least important part, the code can be just shared privately.
In fact, there are many such European code, data and information sharing initiatives. There are meetings and conferences where countries can discuss this on a technical level. The code is shared, just not via public channels.
>The government - and taxpayers - should care that having closed-source software means they are tied to the company that wrote it forever, so changes and bugfixes will be much more expensive.
If a private company owns code used by government for critical purposes and can take the government hostage it's outrageous and taxpayers should riot. This probably happens[1], but most code is either written by government itself, or at least government owns the code and can switch contractors if necessary.
In particular, AFAIR the government code we're discussing right now was written by COI (~central informatics department), which is a public institution.
[1] For example, governments use Azure and GCP, even though - to me - it's clearly shortsighted. Fortunately there was a wake-up call recently, and it changes slowly.