The ones who receive only heaped praises are the dead and the despot.

The short-term opinion is usually not objective. So a (good) reputation could even be a destroying force. Think of some mediocre, forgotten figures suddenly get heaped praises. Or at least they are not attracting attacks. On the other side, psychologically people will suddenly feel a person gets much too more than he deserves but it's the exact same people who used to give the award. It might be the case that some reality pertaining to the guy is revealed but how can you conclude that forgotten-and-suddenly-revealed counterpart is truly morally superior?