I assume it was too impractical to keep a fire perpetually burning in your home to transfer flame

I wouldn't make that assumption if I were you. The hearth was so central to the concept of "home" in antiquity that it is used as a metonym for home. The hearth would not necessarily be left full-blaze all the time, but a small little baby flame or at least coals would be left so that the hearth could be easily restarted by fanning it. If one's hearth went out it was a serious problem, and though flints or tinder could be used to restart it the easiest way to restart one's hearth was simply to borrow a flame from the neighbors--hence the ritual prohibition on providing fire and water to exiles. In the cramped, lightless insulae in which the vast majority of the population lived there of course was no hearth, and the majority of the urban poor in the Roman world could not cook their own meals at home (though communal ovens for baking bread existed) and probably could not reasonably light their own single-room homes, which were little more than places to sleep for them