Spot welder: High current advantage over high voltage
The reason we do this is because there's two resistive components in the system: the arc where we are welding and the transformer itself.  We're looking not just to maximize power in the weld, but to minimize waste.  If the transformer's resistance is higher than that of the welder, then most of the energy actually gets dissipated in the transformer, and the transformer heats up like crazy.  If we decrease the number of winding to decrease that resistance, then we improve our power transfer, but decrease the voltage of the transformer.

There's a sweet spot for each system.  That's where they're trying to aim.  In the case of a welder, that sweet spot involves a step down to low voltage and high amperage.

Also, if you have any control circuitry, controlling the amperage is better than controlling the voltage here.  The voltage drop of the system comes from all sorts of wires and connections.   The resistance of the system, for instance, can drop if you connect more metal surfaces together with good solid welds.  This means that, if you control voltage, you have to pay attention to all of these details, when all you really cared about was "power in the weld."  If you control amperage instead, then your power dissipation in the weld is always \$P=i^2R_{weld}\$, and it ignores all those other details.  Thus, it is helpful to think in current terms.