Great idea! They could call it a "Prius".
Sir, you are uncommonly perceptive. I had not realized that so much development had already been put into the marketplace.
A Prius doesn't do that. Or, perhaps only the latest models do.
Most of the Prius'es use both the electric and combustion engine in a tandem pair to propel the car, not all that different than some of those monster trucks that have more than one engine working in tandem.
The only one I know of (I bet there are others) with an actual generator was the first generation Chevy Volt. Other than at a high rate of speed, the motor was exclusively a power generator no different than the power generator you keep in your garage only for situations when the power is out. The combustion engine in the Volt was only used for driving purposes above 70mph.
If you always stayed below 70mph, the first generation Volt is a 100% purely electric car with a generator, just like a train.
https://www.cnet.com/roadshow/news/chevy-volts-engine-more-than-just-a-generator/