I guess then you don't have a huge problem with vandalism and litter. It is hard to find a public space here where some dickwad hasn't left a beer can, used condom or cigarette butt. We also like to sue the crap out of each other. So anytime someone is on your land, you are subject to getting sued when they get hurt. So I don't blame people for trying to keep other people off their land. It would be nice if we had what you describe. But I think that ship has sailed here.
I think the freedom to roam in general has a substantial impact on reducing this problem - we're taught about these rights in primary school, but also taught about the corresponding duty to leave campsites etc. as we found them, and to be considerate about how we exercise these rights.
Of course, there's always some assholes.
In Norway the concept pre-dates written law, and in its current incarnation it guarantees public right of access to most non-urban land, as well as almost all of the coast line. Basically, outside of urban areas, as long as we avoid peoples gardens, and things like tended fields, we can pretty much go where we want, whether or not it is private property, without seeking permission from the property owner (though it is considered polite to introduce yourself to the owner and seek to take their wishes into consideration if you make use of the rights in the vicinity of where they live).
We can also, with some further limitations, pretty much camp where we want. Further, tradition creates legal rights of access - if a path or a road has a history of public use (20-30 years is a typical yardstick, though frequency of use and the owners actions in the period that usage is becoming established will mattr), that access is legally protected; if a new owner decides to try to prevent continued public access, they will generally face an uphill battle.
The reasoning behind this is basically that allowing a property owner exclusive use of large areas of land would be a massive curtailment of the liberties of the population as a whole, and that maximizing public access to land is a substantially larger net positive in terms of liberty than the relatively limited negative impact for property owners.
It is considered so fundamental in Norway that it was not considered necessary to codify in law until 1957 (almost all of Norwegian law is codified), as it was seen as intrinsic to the legal system. In Sweden, their variation is protected by inclusion in their constitution.