Using normal diodes to rectify high frequency waveforms
Every diode needs some time to recover its reverse resistance after voltage polarity changes. During the recovery time there is high reverse current through the diode. This reverse current makes the diode to produce some heat.
The higher the frequency is, the more time is spent in the recovery state and so the more heat is produced by the reverse-recovery process. Low-frequency diodes (like 1N4007) have relatively long reverse recovery time, and you've seen what it leads to. Higher-frequency diodes (like HER or FR series, for example) have much shorter recovery time which allows them to operate at about 300 kHz.
Using a high frequency diode to rectify a low-frequency waveform will produce even less heat by reverse-recovery than in case with a low-frequency diode, but in both cases it will be negligable to heating by forward-current. So the only drawback of using a high-frequency diode to rectify a low-frequency waveform is the diode's price.