In some songs that I have listened, only one inversion could be used; when one tries to use other voicings, it will sound really odd. So, when it is more preferrable, for example, to use the second inversion than the root position and first inversion, and vice versa. I am specifically asking about the major chord inversions; I'll leave the other chords for other questions.
Example of a song I am refering to: the Hook part of IU - You and I. This songs uses Eb (V) --> Bb/D (I) --> Cm (ii) ... When I try to play Bb/D using Bb as the bass voice on the piano, it sounds really odd.