Is soldering extra wires to increase current capacity on a pcb trace good design?
Soldering wires onto a PCB like that definitely increases current capability.  Whether that's good design we can't of course answer without knowing the design criteria.

Downsides of this method are that it takes significant manual labor in production, therefore will reduce yield because people make mistakes, cause more unit to unit variation than othewise, and won't be as corrosion resistant because there won't be a layer of solder mask over the conductor.

Whether these tradeoffs are "good" or not depends on factors we can't know.  For example, if this board will be manufactured in a part of the world where you can pay someone a bowl of rice and $.50 a day, then it makes a lot more sense than where you have to pay US minimum wage.