What are the implications of "Lo Yasuru Mimenu"?
Rashi (citing Yoma, 72a): It implies a La'av against ever removing the staves from the Aron - which was subject to Malkos. 1
Riva (citing R"M of Kutzi): It implies that the staves should fit tightly into the rings, so that, when those carrying it ascend a mountain 2 , the Aron will not slide down towards those in back, and when they descend, it will not slide down towards those in front.
Refer also to 38:22:2:1*.
Rashi (in Chukas, Bamidbar 20:22). Even though the Anan flattened all the mountains from before Yisrael, it left three - Sinai, Nevo and Hor ha'Har, for Matan Torah and the burial of Moshe and Aharon. Alternatively, it refers to after the cloud went away, following the death of Aharon and Moshe (PF).
Why does the Torah forbid specifically the removal of the Badei ha'Aron, but not of the Mizbe'ach ha'Nechoshes, the Shulchan or the Mizbe'ach ha'Zahav?
Oznayim la'Torah #1: Because besides transporting the Aron, the Badei ha'Aron served the additional functions of containing the Shechinah - which rested 'between the staves of the Aron', and of demonstrating the love that existed between Hashem and Yisrael - in that they protruded from the Paroches like a woman's breasts, both of which applied at all times, 1 even when the Aron was not being transported.
Oznayim la'Torah #2: Because, symbolically, based on a Pasuk in Yehoshua 2 , where the Aron carried those who were carrying it, the Torah saves those who hold on to it. And since one never knows when this will become necessary, the connection between the Badim and the Aron needs to be permanent.
Because, assuming the Badei ha'Aron represent those who support Torah, it teaches us that they should always remain attached to it 3 and not rely on their wealth for their continued success.
How will we reconcile this Pasuk with Pasuk 14 "Veheivesa es ha'Badim ba'Taba'os", which implies that the staves were removed?
Yoma 72a: The staves were able to slide through the rings, and they made them thick at both ends to prevent them from completely leaving the rings. 1
Hadar Zekenim: The primary Avodah was through Aharon and his sons. Once they inserted the staves - in Bamidbar 4:8, it was forbidden to remove them. Here however, Moshe inserted them and it was not yet forbidden to remove them.
Pane'ach Raza: When the Aron rested, the staves jutted out in front until they poked into the Paroches. But when they carried it, they needed to center the staves and make them fit tightly, so the Aron would weigh equally on the people in front and on those at the back
See Torah Temimah, note 19, who elaborates, and who explains that it was possible to remove the staves, but only with difficulty..