Adding 125% to continuous operating current of load also accounts for elevated ambient temperature, and heating of wire and fuse inside box.
Because magnetic/hydraulic breakers don't have a thermal component, I've seen them suggested for 100% of rating (in the case of one where minimum trip was 105% of rating.) Others I see minimum trip 100%, suggesting you might get away with operating at 95% of rating.
Hmm, thermal devices are affected by current squared, so non-sinusoidal current deliver less power but operate closer to tripping. Wonder if magnetic trip is linear with current?