The absence of government just leads to a situation in which some group takes control of a given area. In effect government will then exist again. During the absence of government there will be chaos and rampant crime.
>Besides, there is an alternative model where there are competing groups of people and I can pick the best among them based on price and services.
In the absence of government, what's stopping these groups from simply joining forces into a cartel, getting some armed thugs and making you an offer you can't refuse? History suggests that to be a far more likely scenario. Oligarchy, rather than competition, is the natural state of capitalism.