Edge computing is undergoing a fundamental transformation from monolithic deployments to dynamic microservices architectures with distributed AI-driven inference. This evolution exposes critical weaknesses in traditional Layer 3/4 networking, which relies on static IP addressing, perimeter-based security and location-centric routing policies. As applications fragment into ephemeral components and AI agents are coordinated across trust boundaries, existing connectivity models become operationally complex and architecturally brittle. In parallel, as complexity increases organizations pay an increasing “networking tax” in slower development, higher maintenance and more frequent disruptions caused by the tight coupling between edge devices, applications and network configuration. This paper argues that edge computing requires a paradigm shift toward application-centric connectivity built on Layer 7 identity-anchored service networking and zero trust principles. We identify key limitations of location-based networking in edge environments, examine the challenges posed by distributed AI systems, and propose design principles and an initial technical implementation for application-centered networking that can accommodate the dynamic, distributed nature of modern edge applications.