Say we have a 100VA transformer feeding a bridge rectifier and then straight into a large filter capacitor. The power factor presented to our transformer will be about 0.6 and so we would be able to pull 60 watts DC from our 100VA transformer for it to be fully loaded.
Then we put a big iron cored choke between the bridge rectifier and filter capacitor. And not just any old choke, but an ultra-choke (the dual of an ultracapacitor

) Because of its huge inductance the current through the choke is essentially constant and so the current in the transformer secondary is a square wave.
Seeing the transformer instantaneous current is now constant and not having gaps that need to be filled by current peaks with their consequent I2R losses, could we assume that the transformer losses are even lower than what they would be if the transformer was supplying a purely resistive load? Just how hard could we push the transformer if we used a ridiculous size inductor? What might be the maximum utilisation factor? This is obviously not a practical approach, just a thought experiment.