By 'simple AC to DC converter' I mean the familiar circuit shown in the figure below, where the capacitor C reduces the ripple.
A sufficiently large capacitor can be used in order to reduce the ripple voltage to any desired level. But in The Art of Electronics the authors state that this approach has some disadvantages, one of which is
The very short interval of current flow during each cycle (only very near the top of the sinusoidal waveform) produces more \$I^2 R\$ heating.
I don't understand what is meant by this extract. Does \$R\$ here denote the resistance of the load? What is meant by 'the very short interval of current flow during each cycle'? Does a bigger capacitor cause more wasted energy?