UK officials use AI to decide on issues from benefits to marriage licences
theguardian.com
theguardian.com
https://news.ycombinator.com/item?id=37924712
In addition, "AI" as in traditional, old-school ML, as in statistics. That said, I'd say they're at least on the right track with their transparency initiative.
That's a formidable question. There are many angles to the question, but in this context, it should be underlined that administrative due process is cast in stone in most Western countries. Therefore, the explainability, transparency, and liability issues of AI/ML are particularly severe in the public sector.