Halakhah zu Divrej Hajamim II 35:3

It also seems that that which Maimonides, may his memory be blessed, said that it is elucidated in Joshua is from this verse, but it is not a clear elucidation at all, as we have said. And that which is stated in I Kings 8:1, "And the Kohanim brought the Ark of the Covenant of the Lord to its place, to the sanctuary, to the Holy of Holies" should also not be difficult in your eyes. It is because the Levites were not permitted to enter the Holy of Holies that only the Kohanim brought it in. And [so] the main approach seems to be like the words of Nachmanides, may his memory be blessed, that the entire tribe is fit to carry the Ark; and as it is written (II Chronicles 35:3), "And he said to the Levites, etc. 'place the Holy Ark in the Temple that was built by Solomon son of David, the king of Israel, there is no longer a burden on your shoulders.'" Its matter is also that Israel would have no more need to carry the Ark form one place to another; but it does not indicate that if it were to move it, that it would not be done by the Levites, and this is clear and obvious to all. And [regarding] that which the Sages said (Chullin 24a) [that] blemishes disqualify the Kohanim but years do not, it is only the priestly duties that are not affected by age, but age does disqualify the Kohanim for the labor of carrying, as it does for the Levites (see Mishneh Torah, Laws of Vessels of the Sanctuary and Those who Serve Therein 2).