Mazda is doing something that I think is fairly novel, which is almost exactly what you've described. They've scaled down the rotary engine from their RX cars to a single-rotor and put it into their new EV (almost tucked into the front wheel well,) and letting it act as a 70ish horsepower generator for the otherwise battery-powered car to extend range.
On top of that, they make fun cars. With buttons and knobs on the dash!
I'm glad they're still around doing their thing.
IIRC, the Freevalve tech is like a 30% efficiency hack for any ICE you put it on, and it's a part of how Koenigsegg are managing to squeeze 600 brake horsepower out of just a 2L, 3-cylinder engine.
Wesley Kagan reimplemented their freevalve technology on his Mazda Miata, and it's probably the coolest hobby automotive project I've seen in years. https://www.youtube.com/watch?v=E9KJ_f7REGw
Here's a really cool explainer on the transmission - https://www.youtube.com/watch?v=Hvb6J96KiSM
I just feel like Mazda doesn’t get enough credit for the innovation they manage to accomplish at a truly mass produced scale. It's almost like they're too "normal" to get the attention they deserve.
The tragedy of Mazda is that they already make one of the best cars in the world, but machismo / public opinion prevents too many men from enjoying the full glory of the Miata. But on the other hand, Mazda's refusal to move it beyond 'momentum car' holds it back. If they added ~30-40 horsepower to it, it could legitimately be stealing sales from cars thrice its price.
I suspect the answer is because it's more efficient from a MPG perspective to allow the engine to directly power the wheels, at the cost of the extra complexity of gearing. Converting motion to electricity back to motion is lossy, and even more so if you insert battery storage as an additional step.