The direct motivation of Nebuchadnezzar in sparing King Jeconiah is not known. However, we can discern his motivation from subsequent events that suggest that keeping an heir of David alive, but under the thumb of the Babylonian king would make it easier to manage the large number of Jews in exile in Babylon.
In or about the year 597 BCE, Jeconiah, the young king of the defeated kingdom of Judah, joins the first wave of Jewish deportees to Babylonia. II Kings 25:12. There, he and his family were cared for by King Nebuchadnezzar. James B. Pritchard, ed., Ancient Near Eastern Texts Relating to the Old Testament (Princeton, NJ: Princeton University Press, 1969) 308. In Babylon, Jeconiah became the first exilarch (aka the Raish Galusa) (my transliterations follow ashkenaz practice; you will also find this term spelled Raish Galuta) -- a position of power over the Jewish people in exile that was held only by direct descendants of King David. Among the exilarchs were Judah the Prince, who was the editor of the Mishna and one of the greatest Torah scholars in Jewish history. The position of exilarch with Davidic geneology continued into the 11th century. One of the last exilarchs was Rav Sherira Gaon (ca 900-1000 CE), the author of the history of the Oral Law in Judaism, the Igerres Rav Sherira Gaon, and one of the last leaders of the ancient yeshiva in Pumpedisa, Babylon (believed to have been a neighborhood in what is now Baghdad).
Through the position of exilarch, and by granting wealth and privilege to the exilarch, the Babylonians maintained effective control of their Jewish population in exile. Igerres Rav Sherira Gaon, Ch. 9 (Rav Sherira, at p. 113, states that the underwriting of the office continued until the 8th or 9th Century CE). An argument could be made that the existence of the institution also inhibited the efforts of Ezra, Nehemiah and Zechariah to repopulate Israel when Babylon agreed to make that possible 70 years after the 1st Temple's destruction.