An inertial frame is a frame which respects Newton's first law: an object moves with constant velocity iff it experiences zero net force. We can say the sun is

An inertial frame is a frame which respects Newton's first law: an object moves with constant velocity iff it experiences zero net force. We can say the sun is at rest. Here the satellite accelerates towards the sun; we say that is due to a force called gravity. This is nice and simple. We can instead say the satellite is at rest. In this frame there is no net force on the satellite. But now the sun accelerates, as do the distant stars; why? And how to explain second-order gravitational effects like tides? It's awkward to work in and leads to bad intuition. To extend it to your freefall elevator example: everything inside the elevator obeys Newton's First Law so we are justified in treating it as inertial. Extend the frame to the surface of the earth and we have a problem: we either have to explain what force causes the earth to accelerate towards the elevator, or admit we have a non-inertial frame. Simplest to just say the earth is at rest and the elevator is accelerating due to gravity. However centrifugal force is not all bad, it has a really cool interpretation which yields a powerful insight. Consider a satellite in an elliptical orbit. As it reduces its radial distance to the sun, it must pump energy into its tangential velocity, to conserve angular momentum. So its tangential kinetic energy is a function of its position. Hey, that sounds like a potential! You can just add this "tangential kinetic potential" to the gravitational potential, yielding a bathtub shaped "effective potential." Now we're in 1D, since we're identifying angular effects with gravity. When the radial distance is large, the satellite will accelerate towards the sun (radial velocity decreasing), as it falls down the gravitational potential well. Eventually it begins to climb the "tangential kinetic potential" hill, and starts accelerating away from the sun (radial velocity increasing). In this 1D world, the sun is attractive at long range and repulsive at short range; the turning points are the apahelion and perihelion of the orbit. What's so cool about this is that we've reduced a 2D kinematics problem to a 1D problem (radial distance varying over time) by absorbing the tangential kinetic energy into the gravitational potential energy. This connects planetary orbits to more familiar problems like the 1D harmonic oscillator. The cost of doing so was the appearance of this "tangential kinetic potential;" the derivative of a potential is a force and that's centrifugal force.