Worn axles are extremely common. When things start shifting around with higher power, a soft mild steel axle shaft will wear before a hardened-steel bearing race. So normally, the bearings are fine but 0.001" of wear on an axle will cause wheel wobbling. Incidently, worn spacers shorten the tension stack of the axle assembly, so the nut torque slacks off, thus making things worse. Truing up the spacer(s) faces on a lathe shortens the stack; eventually, the stack gets so short, the splined u-joint adapter bottoms in the axle splines and then, no amount of tightening will compensate.
I used to weld-repair stock axles with too little bearing press-fit clearance from the factory, but its not worth the trouble in these days of (relatively) cheap high-quality, stronger steel replacements that are sized correctly from the suppliers. The proper bearing-to-axle press-fit interference should be 0.0006"-0.0010" and yes- that 4th decimal is important. Also note- some books incorrectly state the axle nut torque should be 300 ft-lbs. In fact, it should be AT LEAST 400 ft-lbs and more is better. That spanner nut will strip on a stock axle at around 1200 ft-lbs, so feel free to add a little torque!