Future networks are anticipated to enable exciting applications and industrial services ranging from Multisensory Extended Reality to Holographic and Haptic communication. These services are accompanied by high bandwidth requirements and/or require low latency and low reliability, which leads to the need for scarce and expensive resources. Cloud and edge computing offer different functionalities to these applications that require communication, computing, and caching (3C) resources working collectively. Hence, a paradigm shift is necessary to enable the joint management of the 3Cs in the edge-cloud continuum. We argue that In-Network Computing (INC) is the missing element that completes the edge-cloud continuum. This paper provides a detailed analysis of the driving use-cases, explores the synergy between INC and 3C, and emphasizes the crucial role of INC. A discussion on the opportunities and challenges posed by INC is held from various perspectives, including hardware implementation, architectural design, and regulatory and commercial aspects.