I don't think it makes sense for a particular European country to develop its own distro, and certainly I don't think a state or county should be developing its own distro either, as it happened in Munich. Munich having to support its own distro is pretty crazy. At the EU level, administrations would get all the support and funding they need, pretty much.
I do think it's probably better to have a EU-developed distro than using Fedora or Ubuntu, though. Ubuntu at least already comes with proprietary software and licenses, so I'm not sure it would be that much better and trustworthy than Windows is in terms of national security. Let's imagine a war between some EU countries and the US in the future - would Ubuntu be free from manipulation? I'm not talking about hacking, which is to be expected, just good old hands greasing or compelling of the company to create malicious code.
Having an EU-wide distro that all administrations use and rely on would also have some other "unintended" but positive consequences, such as states not being as interested in quitting the EU, since all of their institutions rely on the EU distro. It wouldn't be the deciding factor in such cases, but I'm sure it would play a major role.
Now, do I think Munich gave up its distro because it was "too difficult and expensive"? No, absolutely not. The deal-breaker, or should I say "deal-maker" was the fact that Microsoft promised to build a whole headquarters there! And then suddenly Munich switched to Windows.
I strongly believe that without that coming into play, Munich would've just pushed through with the Linux distro, since they'd already been using it for the past 10 years, or worst case scenario they would've switched to Ubuntu and Libreoffice.
Microsoft used this as a PR technique "see, Linux doesn't work! Look at these guys, they've already switched back to us!" But it only happened because they made a major move to convince them to switch back to Windows, but 99% of the public doesn't understand or know that, so they believe Microsoft's PR, which seems to have worked very well, because it sounds truthful, even if Linux being hard to use and whatnot wasn't the deciding factor.
Microsoft did something very similar when it began patent trolling Android OEMs. They knew most companies would scoff at them and their patent trolling attempt, so they first got some highly strategic wins. First they got HTC to agree to pay the royalty, and then Samsung, the largest OEM.
Now you, and 99% of the people who don't know the whole story would say "but that sounds about right, looks like those companies thought Microsoft's patents were real so they agreed to the deal, no?"
Wrong. What Microsoft did was give these companies something very compelling in return - something where the net winner wasn't Microsoft in the deal, but those companies. If I remember right, HTC got free Windows Phone licenses for a while, and Samsung got a similar deal, and also free or very cheap laptop Windows licenses. There may have been other benefits for those companies, too.
So basically Microsoft didn't care it had to pay these companies to accept their patenting deal (however little sense that may make at first glance), because they knew that later they can push the story that these companies agreed to their patent licensing deals, because their patents are real and they are afraid of getting sued by Microsoft. Plus, they'd get to go to other companies and say "Look, Samsung and HTC, the most important players in the Android market agreed with our licensing deal, and you won't? Are you sure you want to go down that path?!"