I'm suspicious that electrics are viable for first stages where performance advantage is less important. For first stages the cost is linear with ISP. Where it's exponential for second and third stages. (X^2 and X^3!!) For instance the Protons's first stage specific impulse is 285, Electron rockets specific impulse is 303. That's totally comparable.

Does metal 3D printing mitigate any of these challenges? Or is the problem a packaging problem where there is a minimum size required for the mechanical parts?

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.

Any good websites or books you recommend to learn more about them?

I remember reading an interview with some NaSA engineers who were reverse engineering the F1 engines used for the Saturn V. He said notable was the amount of welded assemblies vs ones machined using 5 axis mills, and parts created via Powder Metallurgy on modern designs.

http://atlaspressedmetals.com/index.php/pm-advantages/histor...