The question of whether to series the unused contact on a starter suitable for three phase is an old chestnut, if you can find the instructions for the starter some will recommend the series method and some will say it’s unnecessary. As the instructions are usually missing or unreadable I tend to series in the unused contact on the basis that it will do no harm even if it is unnecessary. A healthy motor should have a balanced live and neutral current or balanced phases and should operate the mechanical trip in a nice even way but a failing motor could have unbalanced currents in the 3 phase case or if a single phase motor was losing current to an earth fault then the return current could be different, in these cases you would still want the trip mechanism to operate so the trip mechanism should tolerate just one bimetalic operator tripping it.
Mike