High-dimensional vector data is gaining increasing importance in data science applications. Consequently, various database systems have recently been developed to manage vector data. These systems can be broadly categorized into two types: specialized and generalized vector databases. Specialized vector databases are explicitly designed and optimized for storing and querying vector data, while generalized vector databases support vector data management within a relational database like PostgreSQL. It is expected (and confirmed by our experiments) that generalized vector databases exhibit slower performance. However, it is not clear whether there are fundamental limitations (or just implementation issues) for relational databases to support vector data management. This paper aims to answer this question. We chose PostgreSQL as a representative relational database due to its popularity. We focused on PASE, as it is a high-performance and open-sourced PostgreSQL-based vector database. We analyzed the source code of PASE and compared its performance with Faiss, a high-performance and open-sourced specialized vector database, to identify the underlying root causes of the performance gap and analyze how to bridge the gap. Based on our results, we provide insights and directions for building a future generalized vector database that can achieve comparable performance to a high-performance specialized vector database.