Why were belts of fortified cities important along early modern frontiers?

In the early modern period, the construction of belts of fortified cities along a country’s frontier was a central strategic priority for state leaders. Following the invention of gunpowder and the development of powerful artillery, traditional medieval castles became vulnerable to bombardment.1

To counter this, engineers developed the trace italienne, a system of geometric fortifications that utilized bastions to eliminate "dead space" and provide overlapping fields of defensive fire. These fortified cities served as powerful obstacles to enemy movement, forcing invading armies to engage in time-consuming and costly sieges. By creating a series of these strongholds, strategists could effectively slow an attacker's progress and protect the state's borders, turning frontier defense into a methodical science of engineering and geometry.123