The problem in these environments is often not technical, but human, full of egos, people without competence wanting to be involved in every discussion and gene

The problem in these environments is often not technical, but human, full of egos, people without competence wanting to be involved in every discussion and generally people talking and evaluating systems based on specs for a year without actually testing things. For every one of the systems you mentioned there is a fairly straightforward solution. And even if you can't solve them all you could gradually migrate everything. Oftentimes because of management wanting to push liability to a private party, they don't want to invest into local dev teams, but instead want to buy a big enterprise solution. The VA, NHS and the German systems all have these issues, but it's not because they're public institutions, it's because they work like enterprise.