You can't put a nuclear reactor in a car. You can charge an electric car's battery using nuclear electricity, of course. But if you're just charging a terrestrial battery then nuclear power's attractive attributes for the Moon (like continuing to produce during a 14 day period of darkness) are less salient. Electricity sources like wind and solar power are likely to charge up the car's battery at lower cost.

You don't need batteries if the energy is readily available throughout the route.

Examples:

1. Buses that use capacitors https://en.wikipedia.org/wiki/Capacitor_electric_vehicle

2. Trains / Bullet Trains / Trolleys that could have that energy along their line.

Car dependency could be rapidly reduced if we truly wanted.