Since we do not balance our wheels with bicycles they are all out of balance. When riding with no hands there is nothing to damp out the resonance that occurs at certain speeds where the out of balance condition and the mass of the wheel reach this resonant point. The cure is simple. Put your darned hands back on the bars. Your hands on the bars produces a damping effect where the energy of the resonance is absorbed by your hands and forearms and the bike doesn't shimmy anymore.
THis happens regardless of loose, tight or perfectly set up headsets and wheel bearings but having loose or tight headsets or loose wheel bearings will certainly make the effect more noticable.
On motorcycles where the wheels are balanced we can ride hands off at almost any speed. But the weight of the motorcycle is so much more than the weight of the rider that it's near impossible to steer by bumping our butt around so not many riders will do this other than some stunt riders that have worked hard to master riding that way.