The Internet, at large, remains under the control of service providers and autonomous systems. The Internet of Things (IoT) and edge computing provide an increasing demand and potential for more user control for their web service workflows. Network Softwarization revolutionizes the network landscape in various stages, from building, incrementally deploying, and maintaining the environment. Software-Defined Networking (SDN) and Network Functions Virtualization (NFV) are two core tenets of network softwarization. SDN offers a logically centralized control plane by abstracting away the control of the network devices in the data plane. NFV virtualizes dedicated hardware middleboxes and deploys them on top of servers and data centers as network functions. Thus, network softwarization enables efficient management of the system by enhancing its control and improving the reusability of the network services. In this work, we propose our vision for a Software-Defined Internet (SDI) for latency-sensitive web service workflows. SDI extends network softwarization to the Internet-scale, to enable a latency-aware user workflow execution on the Internet.