It is telling that in ancient times — in the Hellenic world at least — when people left one city to found another they took fire from the central hearth of the city they were leaving to use in lighting the central hearth of the new city. This made the new city an extension in some ways of the older one.
The importance of the central hearth of the polis is that it was a way to provide a “pure” flame to restart the fire of an individual oikos in the case of it having to be extinguished due to the miasma of a death within the walls of the oikos. It is in some ways the symbol of the central hearth of the “Oikos” of the Olympian Theoi, and as such expresses the agency of Hestia throughout the life of the polis and also within the framework of the Olympians.
Hestia is often underestimated by modern Hellenic Polytheists because there is a lack of information about her cultus in ancient times — other than the acknowledgement that she is to be honored at the beginning and end of any rite. However it is this very acknowledgement that is an indicator of how important she actually was in ancient times. One thing that many scholars tend to NOT write about is the “everyday” things that they encounter — because “common knowledge” is not something that most people think would be lost in the event of a major cultural shift.
However, if you look at modern Greek culture, you can still see a remnant of Hestia’s importance in the importance that is given to hospitality. When a guest enters the home, they are offered food and drink — things that are in Hestia’s domain as the hearth is where those things are/were prepared. Even with the cultural shift that occurred due to the forcible Christianization of Greek society, some elements of the older polytheistic traditions remain within the minds of the common people.
This is actually evident in the way that modern Greeks are banding together to help one another during the economic trials the country is going through right now. Hestia is inspiring community even now, whether most people realize it.