There's no reason to have a generator that charges the pack in a hurry. It really only needs to cover the maximum sustained average draw - driving up an extended grade at high speed. That's a lot less than 300 hp - it's probably not more than 80 hp or so at most.
I remember back in the 90's in auto shop we calculated that you'd only need 15-25hp continuous to essentially power all of a car's needs if you could smooth demand for power from the peaks over the length of the trip. It stuck with me as a surprisingly small number, but it mathed out, even including heating and AC. Cars are both larger and more aerodynamic nowadays; I wonder if the amount would still be the same?
Will car owners be allowed to run their (25 hp) range extenders unattended? It could be useful to allow it to top up battery while parked, and the car could detect its in an enclosed garage.
For many 'standard' driving patterns (relatively 'flat' urban commutes with approx balanced medium length up and down grades) there are lightweight optimal solutions for EV's that can minimise both battery pack size (and weight) and the need to draw on a small rotary engine for recharge.
The UK's drone engines come in light and small with models that range from 5 BHP to 120 BHP with 40 BHP being suitable for broad swathe of "typical" driving.
I believe a Tesla can charge its battery pack at approximately this rate.