The evolution of the Na+/K+-ATPase laid the foundation for ion homeostasis and electrical signalling. While not required for restoration of ionic gradients, the electrogenicity of the pump (resulting from its 3:2 stoichiometry) is useful to prevent runaway activity. As we show here, electrogenicity also comes with disadvantageous side effects: (1) an activity-dependent shift in a cell's baseline firing and (2) interference with computation, disturbing network entrainment when inputs change strongly. We exemplify these generic effects in a mathematical model of the weakly electric fish electrocyte, which spikes at hundreds of Hz and is exposed to abrupt rate changes when producing behaviourally relevant communication signals. We discuss biophysical strategies allowing cells to mitigate the consequences of electrogenicity at additional metabolic cost and postulate an interesting role for a voltage dependence of the Na+/K+-ATPase. Our work shows that the pump's electrogenicity opens an additional axis of vulnerability that is likely to play a role in brain disease.