Why did some old cars use both electrical and mechanical fuel pumps at the same time?

I can't tell you specifically for the application you're talking about, but most of the time when manufacturers use two pumps as you describe, one is a lift pump to get the fuel from the fuel tank to supply the mechanical fuel pump which then pushes the fuel into the carb.

You can still see this used today, but with direct port fuel injection. On GM vehicles, there's a separate lobe on the camshaft (for overhead valve engines). The lift pump (or low pressure pump) gets the fuel to the high pressure pump which is actuated off of the cam lobe. From the electric pump, the fuel is pressurized below 100 psi (I don't remember the exact pressure off hand), while the high pressure pump increases the pressure to around 2100psi. The high pressure pump isn't made to pull the fuel from the tank. Anyways, just an example of how what you're describing is still used today. Diesel engines do pretty much the same thing.

As far as cars only using a mechanical fuel pump, the Ferrari you describe is an odd ball for the era. Most carbureted engines only need a mechanical fuel pump. GM's vehicles only pushed ~14psi to the carb. If more than that was used, it would push past the needle seats and flood the engine. I believe most other manufacturers ran pretty much the same. The mechanical fuel pump was more than capable of pulling fuel from the tank as well as pushing it up to the carb. It would sit fairly low on the engine, fairly close to the level of the fuel tank. Once the fuel was to the pump, there wasn't really a lot of work going on to get it from the tank to the pump.