Using batteries to drive turbo pumps for rocket engines has already been tried. The weight of the batteries makes the overall rocket inefficient:
"In comparison to turbo-pumped rocket cycles such as staged combustion and gas generator, an electric cycle engine has potentially worse performance due to the added mass of batteries, but may have lower development and manufacturing costs due its mechanical simplicity, its lack of high temperature turbomachinery, and its easier controllability." -- Wikipedia
> Electric motors are finally getting good enough in performance.
I am not fully convinced, but I think more companies making more innovative rockets is a great thing for humanity in general. After all, it is statistically unlikely that SpaceX has used every single possible innovation in their rockets.
"In comparison to turbo-pumped rocket cycles such as staged combustion and gas generator, an electric cycle engine has potentially worse performance due to the added mass of batteries, but may have lower development and manufacturing costs due its mechanical simplicity, its lack of high temperature turbomachinery, and its easier controllability." -- Wikipedia