Allowing players to delete their previously earned Trophies enables them to re-earn said Trophies if they ever feel like replaying a game in its entirety. It also will remove any reward they earned from the Trophy, meaning the decision is not something they should do lightly.
Alternatively there should also be the option for a player to hide their Trophies if they wish to. This is good if a player wants to reduce the visual clutter on their page and emphasize particular games, along with hiding specific titles they may not be interested in sharing - whilst still keeping all Trophy progress and rewards.