In the West, especially in the United States, even imagining a political or economic landscape that does not include strong private property rights is difficult. It is often assumed as a matter of course that private property as a concept is good, moral, or just. In addition, in the United States the concepts of personal property and private property are conflated and often considered one and the same, despite there being distinctions between the two in many economic theories.
A concept some variations of Libertarianism, such as extremes like Anarcho-Capitalism, fail to account for, or do not spend much time considering, is the defense of said property. Only those wealthy enough to hire on private security would be secure in their property rights. They then face the irony that a security force strong enough to defend property could also decide instead to seize and divide said property amongst themselves rather than continue to 'work' for wages or the equivalent. With no external agency to appeal to this would simply be the state of things.
Thus, private armies requiring private monitoring. The resources and potential of society being poured into mere preservation of property with little to nothing left over to advance or move civilization forward. Even having a small amount of personal property would require constant vigilance and defense. Were you to leave your house to go to work, who would watch your stuff and protect it? Could your house even have windows without bars and heavy doors without complex locks?
What would protect your car from theft after you arrived at work? Would that be one of the new perks of employment - perhaps poor healthcare coverage but they include parking lot guards? Travel would be dangerous alone, in any case. Moving as a group would always be in your best interest. Could you trust your group, however, to not suddenly calculate that betraying you would increase their own personal wealth and utility enough to make it in their best interest? Perhaps sticking to family groups, or other groups with close ties would be ideal.
A return to tribalism with smart-phones seems to be the end result of Anarcho-Capitalism and other extreme forms of Libertarianism. Like wild animals only what you could successfully defend would be 'yours'. Unlike animals you would have material possessions in addition to territory or a home to defend and secure.
Which leads us to the benefit of having a government. While it could be small, satisfying Libertarians need for small government, it would still need to be incredibly powerful. Although, compensation for property enforcers would need to be high, to prevent bribery and corruption, slowly increasing size of government as more oversight is required for the funding allocated to protecting property.
Iterate a bit and you end up with something approximating our current situation. Perhaps a little leaner, with fewer entitlements but no less police or military power. Likely increased policing would be required, as now we have bands of impoverished people with nothing to lose by committing theft and robbery, with no safety net for those who fall on hard times property crime becomes the only method to sustain oneself if employment becomes hard to come by. That or police work.
To conclude, a society founded and under-girded only by competition and a completely open market makes unfettered and unrestricted competition the best way to get ahead. Theft and robbery become viable means to succeed without a heavy police force to discourage those activities. Layer upon layer of oversight is required to keep the police themselves from going rogue or brigand. Without laws any rules become obstacles to be overcome in pursuit of self-interest rather than moral imperatives. In a circle back to animalistic nature, might again becomes right, with might occulted and sublimated into wealth and property.
Most of those who feel they would end up on top would instead be consigned to the seething masses. The unwashed and underfed clambering for scraps and protecting what meager existence they've scraped out with their life.
Welcome to the Anarcho-Capitalist paradise, the Libertarian dream. Hope your gun is fully loaded.