Another ARPG, Grim Dawn, has a "loot filter" feature which disables the text labels and being able to pick up loot below a specified level of rarity. Does Diablo III have any comparable feature?
As noted in the comments, a legendary item called Puzzle Ring has since been added to the game.
Summon a treasure goblin who picks up normal-quality items for you. After picking up 16 items, he drops a rare item with a chance for a legendary.
Additionally the season 28 introduced the 'Altar of Rites' object which requires unlocking a seal with somewhat extensive resource demands; its effect:
Pets pick up and salvage common, magic, and rare items.
another related seal:
Pets pick up Death's Breath [a crafting material].
Both methods allow automating the collecting-and-salvaging process, while a basic 'loot filter' would only hide the dropped loot and leave their resources behind forever.
Unfortunately, there's no guarantee that the feature will be retained after the season ends ends on August, 2023.