The shift toward IoT-enabled, sensor-driven systems has transformed how operational data is generated, favoring continuous, real-time event streams (ES) over static event logs. This evolution presents new challenges for Streaming Process Mining (SPM), which must cope with out-of-order events, concurrent activities, incomplete cases, and concept drifts. Yet, the evaluation of SPM algorithms remains rooted in outdated practices, relying on static logs or artificially streamified data that fail to reflect the complexities of real-world streams. To address this gap, we first perform a comprehensive review of data stream literature to identify stream characteristics currently not reflected in the SPM community. Next, we use this information to extend the conceptual foundation for ES. Finally, we propose Stream of Intent, a prototype generator to produce ES with specific features. Our evaluation shows excellence in producing reproducible, intentional ES for targeted benchmarking and adaptive algorithm development in SPM.