Why don't electric cars have an electric motor inside each wheel?

I’m not an EV designer, but here are 6 good reasons from first principles…

1. Weight. Four motors are heavier than one motor and a transaxle, even with a differential to allow the left and right driven wheels to turn at different speeds while cornering.
2. Unsprung weight. Weight that tracks the bumps in the road costs much more energy to move than weight that is suspended. Wheels are “unsprung”, and motors in the wheels would be unsprung too. You would likely want to put the motor on the chassis and use an articulated transmission axle, unless you made the motor incredibly light. You could still have four motors, but they won’t be “inside the wheels” as in the question.
3. Harsh environment. Wheels tend to get the worst of wet, dust, debris, etc. You’d like to keep this stuff out of your motors. See #2 above for moving the motors inboard.
4. Control. You need to control four motors, instead of just one. More complexity. But more control opportunity too. Think torque management in slippery conditions.
5. Steering. The motors in the steered wheels would tend to compromise the range of steering motion (because they occupy space), and thus could make the turning circle larger.
6. Cost. Four small motors are more expensive than one big motor.

Here are a few reasons why you would put four motors inside the wheels:

1. Perhaps a better way to make a performance AWD than one motor and a 4 wheel power distribution system. (Note that most EVs today drive only two wheels…)
2. Weight distribution. Gets the motor weight low and distributed. But the battery weight is a much bigger deal…
3. Thermal management. Get the heat from the motors out of the body. Not much, but something.