Re: front tires and their effects on wobbling at "high" speeds
If a front wheel wobbled going fast, I would suspect a few things-
bent or cracked forks? (look closely for cracks in the corners where the welds are)
cracked frame? (likely near the head tube, but maybe where the top and down tubes meet the seat tube)
oddly customized forks? (forks modified so that they lack the proper rake and trail)
If you are using knobby tires that could cause some instability too, but not usually wobbling.
It is possible that a tire could suffer a manufacturing defect that caused it to have its weight distributed unevenly, but generally speaking, bicycle wheels and tires don't need balancing. At all. Ever. At any price level. From any manufacturer. In any country.
Bike shops randomly stuck reflectors into the wheel spokes of hundreds of thousands of bicycles for decades, and nobody ever said that the reflectors caused any imbalance problems by being there.