The LootTable tag only works for chests and trapped chests blocks, however it works for all container minecart variants. This means for example loot tables do not work with the hopper block but work with a MinecartHopper:

/summon MinecartHopper ~ ~ ~ {LootTable:"chests/simple_dungeon"}

/setblock ~ ~ ~ hopper 0 replace {LootTable:"chests/simple_dungeon"}