Why can't there be a continuously charging electric battery car....?

That's how car batteries work now. But they don't have enough energy to move an entire car.

They could salvage some of the kinetic energy to prolong its charge but it is nowhere near enough to keep the battery completely charged. It would defy the first law of thermodynamics, you can't get something for nothing

It's like the battery is providing some energy. The generators are siphoning some of that and putting it back. The only way to put put back all of the original energy would be to take ALL of the kinetic energy from the car. But then it wouldn't move.

Generators don't provide energy from nowhere. You may not notice but the generators make the car decelerate once the engine stops pushing it. It's this resistance that is converted directly into electricity. Since you barely notice it slowing the car, it's easy to tell there's not much energy there so it's not enough to totally recharge the car.

The car does have a generator (the alternator) to charge the battery while the car is in motion, but, instead of being connected to the wheels its connected to a rotating part of the engine normally via a belt.

When you were riding your bike you were providing the power to drive the generator for the lights, same thing with the car you have to put some energy in to overcome the losses in the system

ie. friction, wind resistance, back emf in the generators etc. You cannot get something for nothing.