In the case of market economy, if you can't use violence, then the world would be split into natural monopolies and monopolies after market consolidation. Everyone else will be feudalized because someone else will control their access to water, electricity, education or whatever. Because property is sacred and we can't use violence no matter the consequences.
The ever expanding free to enter and free to participate market is a delusion, so let's not delude ourselves that it will take care of everything without us taking responsibility.
I'm not sure what you really mean by "monopoly" or what sort of monopoly you think can persist in the absence of government support.
Note, I started my participation in this thread by advocating for minimizing government, which is not the same as eliminating government. So I'm not trying to assert an absolutist position that free markets should have no regulation.