The current focus of offshore wind industry and academia lies on regions with strong winds, neglecting areas with mild resources. Photovoltaics' cost reductions have shown that even mild resources can be harnessed economically, especially where electricity prices are high. Here, we study the technical and economic potential of offshore wind power in Indonesia as an example of mild-resource areas, using bias-corrected ERA5 data, turbine-specific power curves, and a detailed cost model. We show that low-wind-speed turbines could produce up to 6,816 TWh/year, which is 25 times Indonesia's electricity generation in 2018 and 3 times the projected 2050 generation, and up to 166 PWh/year globally. Although not yet competitive against current offshore turbines, low-wind turbines could become a crucial piece of the global climate mitigation effort in regions with vast marine areas and high electricity prices. As low-wind-speed turbines are not yet on the market, we recommend prioritizing their development.