It's funny because this is exactly the opposite of what actually happened. Mafias are the reaction to the "unification" of Italy, and they almost all come from the previous governments that existed before unification. Northern Italy conquered the south and defeated all the little states there ... and then levied taxes and did not much else. Specifically they did not provide policing, and very few public services.
And then the remnants of the old governments stepped in, provided public services, security on the streets and "pressured" people into paying a second tax. Now you can say that they were almost-feudal governments and therefore defended and enforced the law of large landowners but that wasn't seen as a problem ... because that's how it had always been.
The reason for their success, their initial success at least, is that, first, when Italy was young, it left citizens to their fate, suppressing dissent, stationing small forces in most of Italy that abused locals, were extremely corrupt and did little else. What is generally blamed for their later reputation is that the mafias started using their power more and more for their own purposes, irrespective of cost, while the mafias also pressured the centralized state to do the opposite.
Especially early on it's very hard to pick "the right" side in the war on mafias. In the beginning people saw the mafias as the good guys, and with good reason. Over time mafias became worse and the central state became better, but honestly, the central state wasn't particularly good for people either (in fact it still can be improved quite a bit)