I'm not allowed to be negative, but after thinking about how it might work I thought I'd raise a few UI issues for consideration/discussion/debate/pooh-poohing...:
- The last three-line icon shows, upon a click on it, other nodes like playlists, services, computer, devices.
- Show/hide of left sidebar is auto-handled depending on the selected node like iTunes.
1.
Quickly considering the current options for Navigation tabs available in MusicBee now, I'd say about half of them would need the left sidebar displayed to be efficient and intuitive to use. Anything hierarchical like the playlists, library explorer or computer explorer isn't going to translate well to a drop-down menu/sub/sub-sub menu selection method. In that case, I don't see a toolbar as an improvement over the navigation panel with auto-hide enabled. It may actually be worse, because auto-hide isn't really an option - clicking the Playlist toolbar button will need to display the panel to show the list of playlists - so it may actually result in the navigation panel being shown more often if you use those items regularly.
I'm not sure about the others like Audiobooks, Podcasts and Radio stations as I don't use them, but if they also allow for custom folders and sub-folders the same thing applies.
2.
It introduces a sense of "modality" which seems counter-productive. For example, if you have your music library displayed and want to do something else you have to click a toolbar button to switch to what would effectively be "Playlist mode" or "Filter mode" or "Explorer mode" or "Device mode" etc. in order to then select which one you want to work with. With the current navigation panel everything is one place and it's easy to switch between them with one click.
3.
On the other hand, if you find yourself mostly using the features that are only displayed in the main panel (e.g. switching from Library to Inbox or Play History or any of the Services options) a toolbar with buttons is an efficient use of pixels.
4.
Also, I know it's not the point of your request, but I'd recommend against having the search box left of the tabs. IE 11 does that and I keep clicking on it thinking it's the first tab I've opened! Or maybe I'm just an idiot.

5.
Obviously, if it's added as an option, no one is forced to use it and everyone(?) will be happy - something Apple should have considered in their "upgrade" to iTunes 12 if the Google results for "itunes 12 sidebar" are anything to go by.
Bee excellent to each other...