That’s called a series hybrid and very few cars use that configuration. BMW i3 had a series hybrid version that was discontinued a few years ago, and there was the Chevy Volt (also discontinued).
I don't every want a 100% electric car. We're a 1 car household so I really want the flexibility of going wherever without having to plan around the charger network.
The claimed mileage is similar to Toyota's planetary power splitting thingie, no idea how it works in the real world.
You could also say that hydrogen fuel cell vehicles are series hybrids, since the fuel cell mostly charges a battery, which is much more flexible in what power it can provides and can be recuperated into, unlike a fuel cell which is one-way.