A volunteer fire department would be one logical solution. There are certainly unincorporated areas in the US where neighbors have banded together to support such a function.
A second "libertopia" solution would be the one you suggest - contracting with a private company. And in libertopia, unless you owned the property free and clear, I imagine anyone financing or insuring a house would demand such a contract be prepaid as a condition of the loan or policy.
If you owned it free and clear you might dispense with it, but because libertopia's justice system would be based on restitution, if your neighbor's house was burned because of some action of yours, you might be working for your neighbor for a long time to restore him to wholeness.
Not only will I no longer consider the message, I will work against them.