AA is the process of attributing an unidentified document to its true author from a predefined group of known candidates, each possessing multiple samples. The nature of AA necessitates accommodating emerging new authors, as each individual must be considered unique. This uniqueness can be attributed to various factors, including their stylistic preferences, areas of expertise, gender, cultural background, and other personal characteristics that influence their writing. These diverse attributes contribute to the distinctiveness of each author, making it essential for AA systems to recognize and account for these variations. However, current AA benchmarks commonly overlook this uniqueness and frame the problem as a closed-world classification, assuming a fixed number of authors throughout the system's lifespan and neglecting the inclusion of emerging new authors. This oversight renders the majority of existing approaches ineffective for real-world applications of AA, where continuous learning is essential. These inefficiencies manifest as current models either resist learning new authors or experience catastrophic forgetting, where the introduction of new data causes the models to lose previously acquired knowledge. To address these inefficiencies, we propose redefining AA as CIL, where new authors are introduced incrementally after the initial training phase, allowing the system to adapt and learn continuously. To achieve this, we briefly examine subsequent CIL approaches introduced in other domains. Moreover, we have adopted several well-known CIL methods, along with an examination of their strengths and weaknesses in the context of AA. Additionally, we outline potential future directions for advancing CIL AA systems. As a result, our paper can serve as a starting point for evolving AA systems from closed-world models to continual learning through CIL paradigms.