For my use-case, I use both plugins together to achieve different but harmonious things.
I use Customizable-Sidebar to hide things that I do not want & to add custom commands.
I use Obsidian-Bartender to rearrange icons in the sidebar with quick and simple drag-and-drop functionality, without the need to open the plugin settings to rearrange (as is the case with Customizable-Sidebar), or, as you recommended, having to remove all sidebar icons first and readding them afterwards so that they can be rearranged. Perhaps that makes sense for someone who wants to start fresh and re-add only what they want, one by one, whereas for me, I wanted most of what I had in the sidebar, I just needed easy functionaility to rearrange them.