Levush ha'Badim was commanded to go Beinos la'Galgal and take coals from Beinos ha'Keruvim. Why did he not do so?
Radak (6) #2: He deviated from the command to go there, just like he himself did not take the coals from Beinos ha'Keruvim, rather, the Keruv took. He did not deviate from the Mitzvah [amidst lack of fear of the Commander], rather, like a man who fears to enter a place more elevated and Kadosh than himself. Rather, he stood by the Ofan to see what will be. The Keruv took the coals and put them in his hands.
Malbim (6): Because he was an advocate, he did not want to take fire to burn. This is not his mission, for he is prepared for Chesed 1 ! Therefore, he stood next to the Ofan, for the Ofan and Ma'arachah did not obligate burning the Mikdash. He wanted that Hashem will do Chesed with Yisrael amidst Hashgachah, and also protect the Mikdash amidst nature.
Even if he is prepared for Chesed, if Hashem commands otherwise, he must obey! Perhaps he understood that Hashem does not really want him to do so, just like Moshe correctly understood that "Hanichah Li" (Shemos 32:10) does not forbid praying - just the contrary, it is a hint that prayer will help! (PF)
What is the significance of putting the coals in his hands?
Malbim: The fire was due to Hashem's decree. He put it in the hands of Levush ha'Badim to cool the fire via advocating merit. Amidst this, the Mikdash was not destroyed immediately.
Why did he leave?
