In anticipation of emerging applications such as business services, 5G, and the Internet of Things, research and standardization are working together towards next-generation 25/50 Gbit/s passive optical network access networks. However, the increase in single-channel line rate is limited by the distortion introduced by the low-cost device's bandwidth limit or the chromatic dispersion in the fiber. Burst-mode electronic distortion/dispersion compensation can be used to mitigate these effects, but requires a burst-mode equalizer (BMEQ) for upstream traffic and introduces many challenges. In this invited paper, the feasibility of single-channel, directly modulated upstream 25 Gbit/s non-return-to-zero transmission is investigated in more detail. By using a linear burst-mode transimpedance amplifier together with an offline BMEQ, specific BMEQ penalties and trade-offs such as limited training time and burst-to-burst phase variation are considered.