Can we use ECI coordinates for an airplane?
The basic reason is the goal in navigation.  For an airplane it is to deliver the aircraft to a particular destination on the earth's surface, potentially also avoiding certain areas fixed to the earth's surface.

If you do all your navigation calculations in ECI, you then have to keep track of the earth's rotation to translate that to a point on the surface.  If you do all the navigation in ECEF, then that translation is unnecessary.

Both methods are mathematically valid (for ECEF, you have to have some method of removing or ignoring the non-inertial frame effects like Coriolis; for ECI, you have to keep track of earth rotation).  I don't have any direct evidence, but I suspect that since ECI was not an option historically, the current solutions are robust and no one is looking to create a radically different method for unknown benefit.