Seen a number of threads asking for this.
Would be nice. I have tried games that install a trophy set, then find I can't stand the game and it stays there at 0%. Not a big deal, but the option to flush it would be appreciated.
The problem would then arise where people accidentally deleting trophies that they actually wanted. Then they'd start calling Sony/SCEA by the thousands asking (begging) for the return of their trophies only to be told that they would have to re-earn them.
As the total number of trophies is limitless, the games we don't play will slip to the bottom. And as we continue to play newer games, those older games will be forgotten.