for stick drift, why might desoldering pins help stop stick drift?

I am wondering if perhaps you've encountered the phenomenon known as a cold solder joint. This happens when not enough heat is applied during the soldering process, resulting in an incomplete weld between the two parts. Over time either movement and/or oxidation can cause the incomplete joint to separate, giving you a bad connection - which could be an open circuit or increased resistance.

It's entirely possible that your attempt at heating the solder joints added enough heat to reform the solder correctly in the cold solder joint thereby fixing the original problem.