After GNOME3 came out, one of the common criticisms I heard/read about was that a click on the the terminal icon doesn't start a new terminal - it brings the current one to the foreground.
I wouldn't have noticed, I can't remember the last time I clicked on that icon. GNOME has for years supported setting a keyboard short-cut to fire up a terminal. GNOME3 still supports that short-cut. Go to System Settings → Keyboard → Shortcuts, click on "Launch Terminal". Assign a shortcut (e.g. Ctrl+Alt+T). And that's it. Now you can fill your screen faster with new terminals than you could ever click it.
On that note, I recommend using "Terminator" as your terminal emulator, assign shortcuts to "maximize window" and "maximize window horizontally" and with a few shortcuts you essentially have tiling window manager for terminals, inside GNOME.