Late last year I fitted two new front tyres on the Xantia. Deliberately, I ran them without balancing. The alignment coloured dots were followed.
Tracking was fair; not perfect but not massively wrong.
The results are in - one has completely expired after ten months, the other is well-worn. Vibration was noticeably bad as well. I fitted a part worn from the previous year (stored indoors, and only two years old) and balanced both. The tyre shop have done their dash; whining because the tyres were not virginal and it required an adaptor plate, then overcharging (IMO). Immediately half my driveline vibration went - the other portion is driveshafts, a buckled rim and wheel bearings.
So... Lack of wheel balancing can shorten tyre life.