Large capacitors "producing more I²R heating"?
For a given average current, drawing it in short bursts creates more heating in a resistor than a smooth flow. The reason for this is that current is averaged over time but power is equal to current squared. For example 1A through 1&ohm; for 1 second = 1 Watt, but 2A for 0.5s + 0A for 0.5s is 4W*0.5s + 0W*0.5s = 2 Watts.     

This is why to get the heating effect of AC current through a resistor you must take an rms (root mean square) measurement, not just the average that a meter would normally show. 

Using a larger filter capacitor causes current to be drawn in shorter bursts because the voltage doesn't sag as much between cycles, so the rectifier conducts on a smaller peak part of the AC waveform. If the load draws a fixed current then the average current is the same, but the peaks must be higher. Assuming resistances in the power supply circuit don't change, the power loss will be higher due to the higher rms current.