https://www.aacademica.org/hernan.emilio.tacca/9.pdf

I did some more looking, the linked study says that turbopumps scale better then electric as the burn time increases. Because burning fuel and oxidizer is more weight efficient than batteries. At short burn times that's offset by the increased weight of the turbopump.

Along with my earlier comment, the Proton first stage only burns for 130 seconds. Which puts first stages in the short burn category where eletrics do well. *but never as good as turbo pumps. Which supports the idea that electric systems can compete for large first stages by being simple, cheap, and reliable.

More whack is relanding first stage electric fed rockets. Ala SpaceX.