Electrochemical detection of single molecules is being actively pursued as an enabler of new fundamental experiments and sensitive analytical capabilities. Most attempts to date have relied on redox cycling in a nanogap, which consists of two parallel electrodes separated by a nanoscale distance. While these initial experiments have demonstrated single-molecule detection at the proof-of-concept level, several fundamental obstacles need to be overcome to transform the technique into a realistic detection tool suitable for use in more complex settings (e.g., studying enzyme dynamics at single catalytic event level, probing neuronal exocytosis, etc.). In particular, it has become clearer that stochasticity—the hallmark of most single-molecule measurements—can become the key limiting factor on the quality of the information that can be obtained from single-molecule electrochemical assays. Here we employ random-walk simulations to show that this stochasticity is a universal feature of all single-molecule experiments in the diffusively coupled regime and emerges due to the inherent properties of Brownian motion. We further investigate the intrinsic coupling between stochasticity and detection capability, paying particular attention to the role of the geometry of the detection device and the finite time resolution of measurement systems. We suggest concrete, realizable experimental modifications and approaches to mitigate these limitations. Overall, our theoretical analyses offer a roadmap for optimizing single-molecule electrochemical experiments, which is not only desirable but also indispensable for their wider employment as experimental tools for electrochemical research and as realistic sensing or detection systems.