This paper argues that the growing integration of artificial intelligence (AI) into e-government intensifies a structural misalignment between digital transformation and the capacities required to govern it. Artificial intelligence enables public-sector systems to scale, automate and interconnect faster than the legal, organizational, regulatory and cybersecurity networks needed to oversee them can develop. The paper introduces the concept of the AI pace gap to describe this pace asymmetry within e-government. It then identifies three reasons why AI makes pace misalignment more acute in public administration: 1) accelerated deployment without equivalent institutional redesign, 2) deeper interdependence across public systems and 3) expanded governance burden that exceeds cybersecurity in a narrow sense. The paper concludes that narrowing the AI pace gap requires anticipatory governance, including secure-by-design public infrastructures, adaptive oversight and coordinated institutional capability-building.