The proliferation of fifth-generation (5G) networks has opened up new opportunities for the deployment of cellular vehicle-to-everything (C-V2X) systems. However, the large-scale implementation of 5G-based C-V2X poses critical challenges requiring thorough investigation and resolution for successful deployment. This paper aims to identify and analyze the key challenges associated with the large-scale deployment of 5G-based C-V2X systems. In addition, we address obstacles and possible contradictions in the C-V2X standards caused by the special requirements. Moreover, we have introduced some quite influential C-V2X projects, which have influenced the widespread adoption of C-V2X technology in recent years. As the primary goal, this survey aims to provide valuable insights and summarize the current state of the field for researchers, industry professionals, and policymakers involved in the advancement of C-V2X. Furthermore, this paper presents relevant standardization aspects and visions for advanced 5G and 6G approaches to address some of the upcoming issues in mid-term timelines.