As the energy landscape evolves toward sustainability, the accelerating integration of distributed energy resources poses challenges to the operability and reliability of the electricity grid. One significant aspect of this issue is the notable increase in net load variability at the grid edge. Transactive energy, implemented through local energy markets, has recently garnered attention as a promising solution to address the grid challenges in the form of decentralized, indirect demand response on a community level. Given the nature of these challenges, model-free control approaches, such as deep reinforcement learning, show promise for the decentralized automation of participation within this context. Existing studies at the intersection of transactive energy and model-free control primarily focus on socioeconomic and self-consumption metrics, overlooking the crucial goal of reducing community-level net load variability. This study addresses this gap by training a set of deep reinforcement learning agents to automate end-user participation in ALEX, an economy-driven local energy market. In this setting, agents do not share information and only prioritize individual bill optimization. The study unveils a clear correlation between bill reduction and reduced net load variability in this setup. The impact on net load variability is assessed over various time horizons using metrics such as ramping rate, daily and monthly load factor, as well as daily average and total peak export and import on an open-source dataset. Agents are then benchmarked against several baselines, with their performance levels showing promising results, approaching those of a near-optimal dynamic programming benchmark.