Terrific contribution!
I have an interest in multipoints since there is one near where I live where six borders meet; if we discard one of them (which is a mere boundary of a property), it is definitely a quintipoint, although in administrative terms the units (parishes and precinct) are no longer officially in use. This brings up two important points if we want to assess the incidence of multipoints: (i) administrative borders change, so we should not forget to consider older maps; (ii) the lowest level of administrative units to consider must be property borders. It would, for example, be interesting to run this for cadastral maps. Even if we ignore property borders, administrative subdivision of land varies between countries, which affects the incidence of multipoints.
An unrelated feature is the geographic nature of multipoint: it is of course not a coincidence that many are located on mountain tops. At least at a lower administrative level, lakes are obvious places for many borders to join (quadripoint in lakes are common on Swedish cadastral maps). From the land-surveyors perspective, prominent points in the terrain were preferentially chosen, which is why islands in lakes and mountains were often used where several properties met. When I check cadastral maps of Lake Sommen (county of Östergötland), there are 2 quintipoints and 4 quadripoints on islands. There is also 1 quintipoint in the middle of a narrow strait. For comparison, there are 3 quintipoints and 6 quadripoints located in water. In total: 6 quintipoints and 10 quadripoints in a single lake.
