Such a setup is vastly less efficient for small engines. If the combusion engine is turning, the best way to use that power is directly to the wheels, as opposed converting it back and forth to electricity.
In locomotives, some ships, and now tanks they're replacing the whole drivetrain with copper wire driven by an ICE alternator. Even with zero energy storage this permits a dramatic simplification of the vehicle, and often we're more than willing to pay the cost of mechanical->electric->mechanical conversion efficiency in exchange for losing a bunch of cams, gears, and 90 degree joints that each eat a little energy, take up space in the design, and weigh a significant amount. And it is very often the case that adding energy storage (a very simply bolt-on + software changes) permits dramatically reducing the size of the engine needed.
Separating charge and power deliver requires two motors, a power-harvesting generator connected to the combustion engine and a separate drive motor. Those would need to be electrically separated since they would be always turning at different rates. That means totally separate charge and discharge circuitry, possibly even separate battery banks. Harvesting from the wheels might even require a third circuit to simultaneously charge from two sources. And the drive motor equipment would have to be sized large enough to cover the entire rated power output. Secondly, such a battery-in-line arrangement may create a battery-essential system whereby if the battery failed/discharged/overheated, the vehicle would just stop despite still having a working combustion engines. (The power direct from the generator may not be compatible with the drive motor.)
Modern hybrids bypass all these problems by routing the IC engine to the wheels. The electrical system is then a single motor and an additional sprocket in the transmission. Power is then added or removed through a single motor and associated circuitry with no need to generate and provide electrical power simultaneously (F1 cars used to work like this). Add an extra differential, aka a "hybrid transmission", and you can run either motor alone or together (as in the Prius).
Which is why modern cars are much more likely to include a sixth gear -> drop the rpm, increase the torque = higher efficiency
IIRC A large portion of the carbon created by a car is during the manufacture, so if you're not forging a prop shaft and machining a gearbox, is it acceptable to reduce engine efficiency by some measure? Especially given the engine won't run all the time, just when the battery drop to some margin the car feels it should start charging.
Potentially (theorising here) Your EV will last longer before getting crushed into a cube, as it can compensate for battery degradation, your engine will last longer as it will have a fairly stable usage load (revs etc) and won't be used much