On account of their low-cost, earth abundance, eco-sustainability, and high theoretical charge storage capacity, MnO2 cathodes have attracted a renewed interest in the development of rechargeable aqueous batteries. However, they currently suffer from limited gravimetric capacities when operating under the preferred mild aqueous conditions, which leads to lower performance as compared to similar devices operating in strongly acidic or basic conditions. Here, we demonstrate how to overcome this limitation by combining a well-defined 3D nanostructured conductive electrode, which ensures an efficient reversible MnO2-to-Mn2+ conversion reaction, with a mild acid buffered electrolyte (pH 5). A reversible gravimetric capacity of 560 mA·h·g-1 (close to the maximal theoretical capacity of 574 mA·h·g-1 estimated from the MnO2 average oxidation state of 3.86) was obtained over rates ranging from 1 to 10 A·g-1. The rate capability was also remarkable, demonstrating a capacity retention of 435 mA·h·g-1 at a rate of 110 A·g-1. These good performances have been attributed to optimal regulation of the mass transport and electronic transfer between the three process actors, i.e. the 3D conductive scaffold, the MnO2 active material filling it, and the soluble species involved in the reversible conversion reaction. Additionally, the high reversibility and cycling stability of this conversion reaction is demonstrated over 900 cycles with a Coulombic efficiency > 99.4 % at a rate of 44 A·g-1. Besides these good performances, also demonstrated in a Zn/MnO2 cell configuration, we discuss the key parameters governing the efficiency of the MnO2-to-Mn2+ conversion. Overall, the present study provides a comprehensive framework for the rational design and optimization of MnO2 cathodes involved in rechargeable mild aqueous batteries.