Sodium-ion batteries (SIB) have recently emerged as an alternative to current lithium-ion batteries (LIB), using low-cost and abundant raw materials. However, previous assessments have come to controversial results regarding their economic competitiveness, and the potential impacts of SIB on the wider energy system are still unexplored. This study combines a bottom-up cost modelling including future performance developments on material level for SIB with a global energy system model to obtain a comprehensive assessment of the potential impact of SIB on the global energy-industry transition until 2050. The results show that with recent cost developments and learning curves, batteries are no longer a cost-critical component in the energy system with projected utility-scale battery system capex of 28.5–51.9 €/kWh$_{cap}$ by 2050. SIB potentially outperform LIB on the medium term and are less prone to price spikes and supply shortages. Being a so-called drop-in technology, they could be produced on existing LIB production lines with only minor modifications. Therefore, concerns about supply shortages or price increases can be seen as resolved, since any disturbance in LIB supply would simply trigger a shift to SIB. The overall energy system structure remains virtually unaffected, with similar solar photovoltaic shares, but a shift in power-to-X processes operation. In this sense, electrochemical energy storage is not found to be a limiting factor for the global energy transition. Correspondingly, this work projects the possibly highest stationary battery demand published with a range of 67.9–106.5 TWh$_{cap}$ by 2050, above those in existing cost-optimised energy-industry system analyses.