What does a Hexfred do?

Rectifier conducts until amplitude of AC voltage is lower
than capacitor voltage (just after peak of the sinewave). At
this point diode is reverse polarized and diode current drops
to zero. Unfortunately it will conduct for a moment in
opposite direction and then it will recover back to zero.
Ideal diode should be very fast to minimize current spike in
opposite direction and very slow to recover to zero. Ratio
of time (on negative side) after the peak to time before the
peak is called "Softness Factor" (RRSF - Reverse
Recovery Softness Factor). You want fast diode to minimize
negative current spike, but not the one that snaps back fast
(you don't want narrow spikes).

Amplitude of the spikes produced by rectifier diodes is not as dangerous as the rate of change (dv/dt).  Very narrow spikes will couple to any LC circuit causing ringing, even if inductance and capacitance are extremely small.  Pretty much everything has inductance and capacitance including components like resistors or capacitors, including power supply caps.

rodman99999,   Fig. 1 is incorrect.  For that to work properly it needs grounded center tap of transformer.  

There are Schottkys operating at higher voltages.  60V would not be enough for most audio application since each diode in bridge rectifier is subjected to double reverse voltage making it 30V max.  In addition we need to count for some overvoltage making it probably useful to about 20V.