In Chrome despite the console having its own tab, it is possible to open the console from any tab by pressing the escape key, so you don't have to keep switching tabs.
In Safari, the console sits at the bottom of the developer tools. The escape key is used to toggle visibility of the console log. Executing a command in to the console command line will also open the console log.
In Firefox, you can quickly navigate to the console by pressing either Ctrl, Shift and K on Windows or Cmd ⌘, Option ⌥ and K on Mac.