1. In Divrei Hayamim Alef 23-26 we read that King David assigned the tribe of Levi to tasks in the new (not-yet-built) Temple, particularly singing songs, and serving as guards. Why were these additional tasks necessary, and why specifically at this moment?
From Bamidbar 4 it is clear that the Levites' only task was to carry parts of the Mishkan. This task made lots of sense in the desert, when Israel was wandering and the Mishkan was carried wherever they went. It was less necessary after entering Eretz Yisrael, when the Mishkan was mostly settled in one place, but still could theoretically be moved; on several occasions it was in fact moved. But when David declared that Jerusalem would be the site of a permanent unmovable Temple, he permanently prevented the Levites from doing the only work which had ever been required of them. So as to keep them as a separate tribe actually filling some functional purpose, David had to find new things for them to do. Because the Temple was going to be bigger and cooler that the Mishkan, there was a functional need for new workers (guards). Also, David's own background as a religious musician made him the right person to introduce music into the service (at least more formally than had been the case previously).
2. Question: did the kohanim in the Mishkan and Temple wear tefillin (and/or tzitzit)? The Rambam says yes (Hilchot Klei Hamikdash 10:2). But do you ever see tefillin being worn in the beit hamikdash picture books? I don't think so. (Perhaps other authorities disagree with the Rambam, I haven't checked.)
From a philosophical perspective, what is the purpose of tefillin/tzitzit? What is the purpose of the Temple garments? Do the answers to these two questions influence our opinion on whether both were to be worn simultaneously? Does the halacha of priests wearing tefillin affect our understanding of the purposes of tefillin and Temple garments? I have no conclusions. Just food for thought.