i'll have to raise issue with your disagreement. consider a thought experiment wherein your rocket ship leaves earth via overcoming escape velocity [noninertial frame], then moves at constant velocity toward the sun[inertial frame], then gets caught in suns gravity well and accelerates toward it [noninertial], then you break away after going once about it and end up in uniform motion away from it [inertial].
mathematically you are perfectly capable of modeling this motion by a series of transformations, each acting on the body of the rocket from liftoff to deep space.
inertial frames absolutely can be transformed into noninertial ones, and back again.
edit: this from a wiki on noninertial frames - 'Measurements with respect to non-inertial reference frames can always be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration is seen from the inertial frame.'
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