Is it important for children to wear "bike" helmets, even when they are only riding a tricycle, big-wheel, or scooter?

Yes: The one foot fall from a tricycle can cause concussion just the same as a four foot fall off a big bike. It's not the height of the fall that damages, it's the sudden stop which is the same no matter the height. The other thing to consider is that kids who wear a helmet from day one are much less likely to put up a fuss and refuse helmet usage when they advance to a big bite. It's just always done