Resistance is a function of cross-sectional area of a conductor. Current capacity is a function of resistance, length, and heat dissipation (largely surface are

Resistance is a function of cross-sectional area of a conductor. Current capacity is a function of resistance, length, and heat dissipation (largely surface area). The cross-sectional area of a copper trace is on the order of ten micrometers square. The cross-sectional area of a solder joint is usually on the order of one or two square millimeters, if not more. For a BGA ball, you can approximate it as a cylinder with radius equal to the ball radius. Again, this is on the scale of millimeters. No matter what, your solder joint will have an order of magnitude larger area than the trace feeding it. Solder joints generally have far lower resistance than a copper trace due to this fact. Besides that, many (most?) lead-free solder alloys use silver, which is famously quite a remarkable conductor. Cold joints and the other problems you mention are basically irrelevant electrically. They're mechanical problems that are likely to cause a break in the circuit. Any added resistance from inclusions or crystal structure are completely irrelevant unless you're doing something extremely specialized like high sensitivity metrology or crazy RF stuff.