You're right. Governments have gained the power they have because they offered people a better alternative. I read somewhere that Napoleon was welcomed as a conquerer into parts of Italy because his government was a lot better than the local government. The problem with governments, though, is that they are fairly easy to establish, but, because they claim a monopoly on coercion, they are hard to replace when a better alternative appears.

For example, all of a city's private garbage collectors may do a poor job, so a very capable mayor may convince residents to allow the city to do the collecting. Years later, when situation is reversed and the city is doing a poor job in comparison with private collectors, it will be a lot harder to replace the government collectors with private ones. The correct response to poor private-sector service is not to bring in the government, but to bring in more private competition.