On-demand ride-pooling has emerged as a popular urban transportation solution, addressing the efficiency limitations of traditional ride-hailing services by grouping multiple riding requests with spatiotemporal proximity into a single vehicle. Although numerous algorithms have been developed for the Ride-pool Assignment Problem (RAP) -- a core component of ride-pooling systems, there is a lack of open-source implementations, making it difficult to benchmark these algorithms on a common dataset and objective. In this paper, we present the implementation details of a ride-pool simulator that encompasses several key ride-pool assignment algorithms, along with associated components such as vehicle routing and rebalancing. We also open-source a highly optimized and modular C++ codebase, designed to facilitate the extension of new algorithms and features. Additionally, we introduce a family of swapping-based local-search heuristics to enhance existing ride-pool assignment algorithms, achieving a better balance between performance and computational efficiency. Extensive experiments on a large-scale, real-world dataset from Manhattan, NYC reveal that while all selected algorithms perform comparably, the newly proposed Multi-Round Linear Assignment with Cyclic Exchange (LA-MR-CE) algorithm achieves a state-of-the-art service rate with significantly reduced computational time. Furthermore, an in-depth analysis suggests that a performance barrier exists for all myopic ride-pool assignment algorithms due to the system's capacity bottleneck, and incorporating future information could be key to overcoming this limitation.