At least it isn't Yellowstone

That gets me, too. Maybe a thousand years ago one could excuse people building in dangerous areas, but they still do. That area isn't an obvious mountain like most volcanoes - the name Campi Flegrei (Phlegraean Fields in English) literally means "fiery fields" - but the earth is hot when you dig down even a bit and there are lots of very hot springs and steam fumaroles. The earth regularly rises and falls (some Roman and Medieval ruins in the area are now below sea level). It has been rising the past several years (magma on the move), with the city of Pozzuoli having risen over 1 foot over the last few years, which I suppose is why they are concerned.

The abundant hot water in that area attracted the Romans, who of course, built baths and spas. The emperors used the town of Baiae within the caldera as a seaside winter resort: the Las Vegas+Beverly Hills+Monaco+Hamptons+Malibu of the age. Caligula ordered construction of a 3-mile floating bridge across the Bay from Baiae to Puteoli at enormous cost, reportedly just so that he could ride his chariot across the bay (perhaps to win a bet and/or out-do Neptune, whom he considered to be a rival god to himself). Feat accomplished, the bridge was then destroyed. The remains of Claudius' banquet hall, where dishes were floated down a central pool to the diners, are there. Nero later designed a self-sinking yacht at Baiae to rid him of his mother where he could watch from his villa (she survived; so had be assassinated by more conventional means). By the Middle Ages, the surrounding area had sunk so far as to become malarial swampland. That town now sits mostly underwater. Even more modern houses in Pozzuoli, a bit further north in the "Fields" have become uninhabitable due to shifting earth and noxious gases over the last several decades. Even with all that, the region has become densely populated over the last century - it will be a major disaster when an eruption eventually occurs.