It is not impossible for a government to act as a mafia (see Russia). But I believe it's impossible for a mafia to be a functional government, they are just built on different grounds.

For me a functional government has the wellbeing of its citizens as a mission. There might be different opinions on how that would look like (hence democracy) but the idea is that; once the government is unchangeable and only cares about maximising the profits of its cadre then it starts becoming more and more like a mafia, just a legalised one.