It was actually more the case that the B battery was the "main" battery, and the A and C batteries being there just for the tubes. The A battery was for the cat

It was actually more the case that the B battery was the "main" battery, and the A and C batteries being there just for the tubes. The A battery was for the cathode heater/filament - it was the one that needed to be big, since its job was to create a lot of heat - and the C, if present, was for grid bias. The main positive rail would be called B+ in a schematic, even for mains-powered equipment, the same way that Vcc is used in transistor circuits.