The only car I know of that works this way is the BMW i3, which came with an optional 'range extender' that's essentially a little gas generator with a 2(!) gallon tank. One complaint I've heard is that it doesn't necessarily put out enough wattage to fully drive the car under certain (hilly, cold) conditions (But, I have to imagine that could be solved with a bigger generator).

The problem as I understand it is that California's regulations require that the range extender doesn't provide more range than the car's internal battery. How this ended up the case I have no idea.

You can convince the i3 to believe it's a European car which increases the range extender's utility dramatically. You can unlock more fuel as well as have the generator turn on whenever you want (as opposed to at only very low SOC), largely mitigating hills.

The purpose of the small gas tank was to qualify for California subsidies and ZEV credits. California doesn't want to subsidize anyone who might buy a PHEV or BEV with REX and then run it 100% on gasoline.

> Why doesn’t this model work in cars and allow us to get rid of the transmission

Nissan e-Power system does exactly that, but requires full EV powertrain. Added cost. Also punishes transmission suppliers.

> Why wouldn’t a hybrid run the engine at exactly that RPM to generate the best charge?

Toyota THS system kind of does this. Output shaft is driven at a speed that is function of resistance and generator RPM and engine RPM thereby allowing RPM to stay in optimal-ish area.

The more I think about future drivetrains, the remarkable and more remarkable Prius starts to look for me - everyone hates hideous Toyota aesthetics and so do I, but Toyota hybrid system is rather ingenious and really something.

It doesn't work because of energy loss converting mechanical to electric and back is higher than mechanical transmission straight to the wheels. Honda does do something like what you describe at low speeds but the efficiency is not very good. Toyota and some other manufacturers use clever arrangements of planetary gears + motor/generator to keep the engine closer to optimal parameters independent of wheels. I'm not sure a modern hybrid system is more complex than a modern automatic transmission.

Somr hybrids do, they're called "series hybrids" as opposed to "parallel hybrids" or may be referred to as Extended Range Electric Vehicles (or some other ordering of those words.)