If the street was left open to the public for year and a day, it would become a public street.

That is the rule thru most of New England ... When I lived in Massachusetts there was a plot of land on a corner that we all used for a shortcut ...it was and is actually private property.
Once a year, generally in the autumn after the tourist have gone home, the sawhorses went up for a couple of days and blocked the area so you could not use it. Thereby keeping the street private property.
This is always done when there is no snow ... I was told by a Legal Eagle that the blocking off has to be done when access is available, rather than just inaccessible because it's covered with three feet of snow and they hadn't gotten around to plowing it.
Along the New Hampshire seacoast there houses that are built abuting the ocean front so there are "public footpaths" for access to the beach through private property. They were established by usage over many, many years. These days the two houses abutting a public footpath often put up fences or plant rows of bushes to delineate the path. The footpaths are kind of a local secret....no signs of course ...especially where they go through the rich folks' properties! Gives us residents a shot at a beach that's not over run by tourists (oops, sorry) I mean visitors. It is a very SHORT coastline