Question: One of the comments on [this question](https://mechanics.stackexchange.com/questions/18623/mileage-varies-by-driving-at-different-speeds) reminded me of something I've been wondering for a while. Given that engines get the best efficiency at peak torque, why do most hybrid cars still use a mechanical transmission (which requires the engine to change speed with roadspeed, as in a conventional car), rather than electrical, with the engine running at a constant rate as a generator?

Is it simply a case of giving people what they are used to? bearing in mind that pure-electric cars obviously have electric transmission...

Trains have been using diesel-electric transmission since at least the 1950s, so it's not exactly a new concept...

Answer: 
It depends on the type of hybrid car you are talking about. In one type of hybrid, there will be a gasoline engine and at least one electric engine capable of driving the wheels. In this case, the gasoline engine must still use a transmission because it cannot be revved too high without causing major damage or shortened life. One possible solution to this transmission issue would be to use a Continuously Variable Transmission (CVT), which can be more expensive to manufacture but keeps the engine at peak efficiency.

The other type of hybrid, where the wheels are driven entirely by electric motors (and has a gasoline generator to charge the battery) does not require a transmission because electric motors have a very wide range of acceptable RPM. Additionally, electric motors have a relatively flat torque curve and the max torque is available instantly. I should note that this type of "hybrid" car is generally just called an electric vehicle (EV) since the gasoline motor is used to charge the battery only and does not drive the wheels.

I was going to comment this, but don't have the reputation:
The diesel-electric transmission you referred to is more closely related to today's EVs in that a diesel engine charges batteries, which then in turn power electric motors at the wheels. Transmissions in trains are impractical for several reasons (such as need to power up to four axles and the number of gears that would be required to keep it at peak efficiency) and this eliminates the need for a true transmission.
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.