I have found so many sources where KV is explained incorrectly.

KV does not mean the rpm increase per Volt.

When the motor spins, there is an electromagnetic field that is created, and that generates voltage in the motor’s coils. This voltage is proportional to the rpm of the motor. The voltage generated is called the back emf. Since the back emf is proportional to the speed of the motor, you see it expressed as rpm/v.

This is NOT the same as kV.

kV gives us the relationship between the back emf constant, and the motor’s rpm. So a 2800kV motor will give you one volt of back emf if it Is spinning at 2800rpm.
Using kV as rpm/v will only give you a rough estimates for the motors rpm at a certain voltage.

Fun fact, the Torque in newton meters per Amp is equal to the kV or Volts/radian second.

I think the over-simplification is just to make it a more understandable concept for less academic audience.
Maybe it just needs to be re-worded a bit, like, the KV value of a motor is a guideline to tell us how many RPMs a motor will give us per volt. And it can vary by around 100kv up and down.