Simple AC to DC converter: upper limit for the capacitance of filter capacitor?
I think there is an unspoken assumption that as the capacitor value increases the load voltage and current will also increase, which would be true if the load is truly resistive. In that case, the ac input waveform can only supply energy to the capacitor when the rectified ac waveform has a higher voltage that the capacitor voltage. As the capacitor voltage increases there is a smaller and smaller part of the ac cycle that has enough voltage to forward bias the bridge rectifiers and add charge to the capacitor. Therefore, the average current during these short times goes up, and the \$I^2R\$ heating during those short times goes up.

However, it's not clear to me that the average power due to \$I^2R\$ loss will go up significantly. I know that many people worship the TAoE but I have found it hard to read and confusing in places.