Interesting fact: in the US, riders without helmets receive more average buffer space from road vehicles than those with.
If you're downhill mountain biking, wear a proper helmet. If you're racing in Manhattan, wear an equally suitable helmet. If you're leisurely riding on a wide, empty side road in a residential area and cycle often, it may lend more placebo overconfidence to the rider than it confers necessary protection. It seems like gearing-up in knee and elbow pads to go for a simple walk.
Please read the linked article, you may find it interesting.
Many things can "break your skull", and there are many things you can do to improve safety. A whole bunch of years ago the then-UK government tried to promote "pedestrian helmets". No doubt this improved safety, but they were widely mocked. You need to draw a line somewhere.
The line is drawn around your bike. Don't ride it without a helmet.