There are, in a way, three categories of games that do this.
Games like Diablo and Borderlands have very limited space and the vast majority of the drops are junk. However, the interest comes from the randomness of the stats of the items. Sure there are some named items with consistent stats, but the vales themselves vary enough that there is no one single item to strive for. For a game like this, there needs to be junk items, but I agree that sometimes they go too far. Nobody loots the common items after a certain point, and even the higher rarities become ignored after a while. Sure it looks cool when enemies explode into white-named items, but you're only going to loot that one rare.
Games like Monster Hunter and Warframe have rather expansive inventories, but the majority of the game is spent looking for rare resources and such to craft exactly what you need. You're progressively working towards getting your resources high enough to get that specific item that you want. If there are rare items/resources, they're usually the gateway. For games like this, the 'common' resource often becomes too common and completely ignored. The 'gateway' materials and blueprints are what the game is all about.
Finally, there are many of the classic MMOs like WoW and Everquest that have specific items that people grind for. You know the stats, you know the boss that drops it, you just kill and kill until you get what you want. Games like this often have currency drops as well as "vendor trash". Unlike Diablo/Borderlands, your inventory is large enough that you can hold a ton of vendor trash that you later turn into money. Similar to MonsterHunter/Warframe, you still have gateway materials, but the "material" happens to be the item itself. Many other items tend to drop which encourages an economy. Games like Guild Wars 2 have high value on the higher rarity otherwise unusable items only for their use in salvaging and "transforming" (Mystic Forge) into more valuable weapons.
In the end, I think that 'common' trash items in Diablo/Borderlands-style games is purely out of visual appeal. Enemies explode into tons of items, and your inventory is too limited to care about the commons. This is arguably unnecessary. Games like MonsterHunter/Warframe tend to have 'common' materials that are all too prevalent and ultimately ignored in favor of 'gateway' materials. The 'common' materials are arguably unnecessary and only hinder the newcomers.
It's in classic MMOs that 'common' items have their place. They're vendor trash. Even suboptimal items can still have value in the player-to-player marketplace. It rewards inventory management. You often have enough space to hold a bunch of items, but you're encouraged to keep your inventory free for junk. In games like this, looting endless junk has a place. It's part of the appeal. Plus, you can always give that stuff to alts, friends, etc. Sometimes even the junk looks nice and you can transmute/transmog the aesthetic onto better statted items.