Hi Toby,
Thanks for your post. Unfortunately this is a tricky one. Controls like the Product Browser, Properties Grid and Available Symbols Palette, i.e. things that you only see when in a drawing, are subordinate to the Drawing Window control (and by 'control' I mean a User Interface element). This means that there isn't just 'a' Product Browser: there is a Product Browser per drawing, and each can have its own state, location etc. It also means that when the main application Window is showing a control other than a drawing window, e..g the Project Dashboard or Products View, display of controls that belong to the drawing control isn't valid.
To head in the direction you want there would need to be some pretty radical root-to-tip changes in the application's architecture. This isn't just a very significant change, it's also rife with opportunities to introduce problems due to the interconnected nature of the application and projects, views and controls. This task, therefore, isn't something we can commit to in the short- to medium term.
Sorry that we can't give you a "yes, of course!" in this case.