I don't think the accepted answer answers this question acceptably. The reason for hybrid vehicles having a mechanical power transfer pathway is that mechanical power transfer has a higher efficiency than electric power transfer.
I have read somewhere (but cannot find the source right now) that the electrical power transfer pathway is approximately 70% efficient in Toyota Prius. To understand this low efficiency, consider that it has a motor-generator operating as a generator, power electronic components, cables, and a motor-generator operating as a motor. Quite many components. This efficiency is considerably lower than the efficiency of the mechanical power transfer pathway.
Actually, Toyota Prius has both mechanical and electrical power transfer pathways. It has a gearbox with one speed and constant ratio but three axles, two of which have electric motors. Changing how much power will be transferred through the electrical pathway changes the relative speeds of the input and output axles, and thus it functions as an electrical continuously variable transmission (eCVT).
The reason for the mechanical pathway is the higher efficiency. The reason for the electrical pathway is that it allows CVT operation with very low cost of components and higher reliability than traditional CVTs. And, also to provide regenerative braking and power boost to the internal combustion engine from a battery.
Have you seen water cooling in a conventional manual transmission? Probably not. However, the inverters in Prius are water cooled due to the high amount of waste heat produced. This illustrates that inverters are less efficient than mechanical transmissions.