An additional benefit of three-phase generators is that they can produce either single phase power or three-phase power. The structure of a three-phase system is represented here. The star or wye (Y) connection provides two types of voltages: line-to neutral and line-to-line. Line-to-neutral provides single-phase voltage and line-to-line provides three-phase and single-phase voltages. A load that requires single-phase power is connected line-to-neutral or line-to-line and a load that requires three-phase power is connected line-to-line. In electricity distribution system, consumer wants both single phase and three phase system, because lighting or small appliance are single phase load but maximum motor (above 3HP) are three phase load. Three-phase generators are more economical and more efficient. Note that all big or industrial generators readily accept both single phase loads and three-phase loads at the same time. A three-phase system requires about 3/4 the weight of transmission line copper as single-phase to produce similar voltages, have similar capabilities, etc.
So three-phase power preferred over single-phase power in Generation, Transmission and Distribution system.