Took me quite a while to find a way to do this, because the default Gnome menu bar is not very intuitively customizable (you can’t drag and drop System into Apps, and Places is nowhere to be found in the customization window), and yet that’s how I first conceptualized what I was trying to achieve should be done.
But you’re not meant to be able to combine these launchers into one on your own; instead, you need to remove the entire menu bar from the panel and then replace it with the Main Menu applet (from the Add to panel
window). The Main Menu combines all three menus under one launcher, visualized with the Ubuntu circle logo by default.