My big complaint with centering cheap single pivot side pulls is the slop between the spring and the slot it sits in. The centerbolt has a part along it's length which doubles as the spring holder and the pressure point for both frame mounting (on one side) and arm mounting (on the other side). (What this part of the center bolt is called is beyond me other then "spring holder"). If the slot in this spring holder allows the spring to move about then keeping the brake centered will be difficult. You see it's the center section of the spring, the portion held in the spring holder's slot, that determines which side of the spring (and the associated arm) move how far from the rim. So any free slop/movement of this portion of the spring will mean that the arms/pads will also not maintain their location consistently.

On well made calipers the spring fits snuggly into the slot and by rotating the center bolt then locking this rotational Aspect in place one can control how far from the rim the two sides are. many better calipers have a pair of flats cut into the center bolt spring holder (Campy's NR as example) or the end of the center bolt has a wrench fitting on it (some Shimano and Weinnman examples) to help hold or fine tune the center bolt's rotational aspect.

But cheaply/crudely made calipers don't usually have these centering aids and the sloppy spring holding nature make these brakes a pain to center consistently. I have further tightened the spring slot up by careful bending the slot's end parts in. But I also have broken the end parts of the slot before, as many times it's made of brittle cast AL.

Running more rim/pad clearance is a common technique to eliminate pad rub in these cases. In the end as long as there's no rub during non braking it really doesn't matter if one pad is closer to the rim then the other. Expect for those of us who suffer from symmetrical system OCD. Andy. (Who goes through life looking at the vertical surfaces and edges about the world to see if they all line up. )