Nothing to do with bypass ratio. Look at photos of, say, F-86 and B-47, both powered by straight jets. Black smoke is unburnt carbon from incomplete combustion. The US engine technology of the time was not capable of full combustion. Compare British engines of the same time, e.g. Derwent, Ghost, Avon, Sapphire - little or no smoke because of better combustion technology.
Generally agree
The smoke thing was a nusisance visually like chemtrails
but of more serious concern in the military.
From an engine cycle effiicency (lb of fuel per lb of thrust per hour) it had little impact.
The designers addressed it by moving holes arround in the burner cans inside the engine. In the end, same internal pressures and temperatures and same fuel efficiency, just turned up the heat in local areas inside the burner.