A blueprint for ultra-low latency in 5G cellular networks is designed to enable ultra-reliable low-latency communication services that require fast delivery of small data units (e.g., packets or frames). However, futuristic applications that are envisioned to be time-critical demand much more than what this blueprint can handle because their data units are typically very large. As the data size increases, the latency is greatly affected by how much data the network can transmit per unit time (i.e., bandwidth). This impact of bandwidth on latency brings the need to guarantee the bandwidth required to keep the latency within the desired time. In 5G, network slicing is introduced to guarantee performance, but how to handle the inherent nature of changing data unit size and radio channel quality over time remains an open question. In this article, for a detailed understanding, we first discuss end-to-end latency at the application level from the perspective of first-byte delay and transmission delay for the remaining bytes. We then investigate how recent techniques relate to end-to-end latency reduction, and present challenging issues caused by their inherent natures. To handle the issues, we propose a new design for next-generation (6G) cellular networks to provide performance guarantees, and discuss open issues in our network design.