Rashi on Numbers 7:9/רש"י על במדבר ז׳:ט׳

1כי עבדת הקדש עלהם [BUT TO THE SONS OF KOHATH HE GAVE NONE (NO WAGGONS)] BECAUSE THE עבדת הקדש BELONGS UNTO THEM — (not the service of the Sanctuary devolved upon them, but the service in connection with) carrying the most holy objects: the ark, the table, etc. was incumbent upon them, therefore בכתף ישאו they should carry upon their shoulders (not in wagons).