Regarding falling, in addition to having more brittle bones than kids, adults are also falling from a greater height, with greater mass.

Along the "scooter" idea, my 5-year-old just learned to go without the training wheels last summer, and at the same time, we got him one of those little Razor scooters. We think that the scooter helped his sense of balance with the bike, too. So that's another option, although just wheeling along with the bike is probably easier.