I like your idea, about kingdoms under suzerainty of the empire, however maybe kings should have somewhat more obligations to the empire. The historic example is the kingdom of Bohemia in the Holy Roman Empire, which position in the HRE is described in the
Golden Bull of Sicily (where the hereditary royal title of the ruler of Bohemia was confirmed).
However a succession crisis in the subject/mediatized kingdom should give the suzerain Emperor an opportunity to intervene. For instance when the Premyslid dynasty died out in the male line, king of the Romans Albert I of Habsburg seized Bohemia (and Moravia) as reverted fiefs of the empire, he made his son Rudolph king of Bohemia, but he died during a siege (dysentery). Later his successor as king of the Romans Henry of Luxemburg (later Holy Roman Emperor) got his son John for whom Henry had arranged a marriage with a Premyslid heiress, elected as the new king of Bohemia.
Another example were conflicts between the Bohemia and the HRE, a defeated king of Bohemia got his territories (Bohemia and Moravia) back as fiefs of the Holy Roman Empire; for instance when Ottokar II of Bohemia was defeated by the empire (ruled by king of the Romans Rudolph of Habsburg)..
However OTOH the situation inside the Holy Roman Empire should perhaps be different from other examples; perhaps the emperor should have opportunities to intervene in a kingdom outside the HRE, which has the emperor/empire as suzerain.