Watching this incredible B-29 Superfortress flight, I was amazed to see that it required a dedicated person to manage the 4 engines and their power levels.
Why was the throttle not placed between the two pilots, like the modern airliners of today?
This setup was actually pretty common for four-engine aircraft of the day. Look at the cockpits of airliners from DC-4 to Lockheed Constellation, and you'll always see a dedicated flight engineer station -- not to the level of managing throttles (which would require a voice command from the PIC to change power setting, impractical for the reaction times required in flight), but to manage the relatively complex and failure-prone large radial engines. The flight engineer station persisted well into the jet era -- at least to the early versions of the 747, which first flew in 1969.
However, if you look closely at a B-29 cockpit, you'll see each pilot has an individual throttle lever set -- they're not between the yokes because of the crawlway for the bombardier station. Rather, they're outboard of the seats, near the (presumably pitch) trim wheels. There were also propeller controls, though they're harder to identify in a cockpit photo. With constant speed propellers, the only control required on an immediate basis was throttle (the flight engineer managed synchronization), and both control seats had throttles, as well as the ability to feather a dead engine.