What about a customizable left menu?

I’m not sure I understood your proposal.

By now, the left menu has a search box and varies depending on what modules are installed.

IMHO allowing the left menu customization is a double-edged sword. Having different screenshots from users does not ease the documentation and support team job.

Moreover, the UI does not persist the view state at this moment. Developing a persistent view would require a non-trivial effort.