The system you speak of sounds like J.S Mill's liberalism. Which basically leves laws that protect the rights of individuals with reguards to themselves, but abolishes any control the government can exersise over individuals.
When it comes to practicality, weather its libertarinism as you described it or anarchy is is simplly not functional. It is probably the most morally correct system (kant, kant, kant) but the fact is that people are basically selfish, the first concern is always for one self and only later do we consider the good of others if at all. A completly free market wil lead to a small number of monopoly firms owning everything (we are not to far from this now) because competition eventually becomes imposible if there are no anti monopoly laws. The rich will be rich and the poor will be poor.
When it comes to functionality i would say that a system that would work best, would be a conservative socialism, with hight taxation, a strong social safety net, a free market with some basic laws ensuring competition, and low or no imigration.