Equipment is so integral to the RPG genre and is so lost on many these days that I'm not even sure I should do this but I will.
First off, how does a hero survive? Well he survives on mainly 2 principles, that folks will reward him for successfully helping him and that he will acquire pricely objects while scouring the darkest and most dangerous corners of the world. And to scout the darkest most dangerous corners of the world he first has to be sufficiently equipped to handle such locations.
So, inventory first comes into play when you are deciding a trip. What should I bring, what kind of extra items do I need, should I pack light so that I can carry more loot or should I pack heavy so that I don't risk getting stuck somewhere.
Once you are in a dungeon, inventory should come into play with how you handle encounters. Can I take that monster on head first, do I have anything that can hit at range, can I lockpick these chests, can I deal with poisons, how long can I last, I risked leaving my best undead weapon - but this dungeon is full of undead.
And then once you start acquiring loot, ultimately another aspect should come into play, often known as item tetris but in its raw format was usually simply based on numbers alone. This is where, as you acquire new loot and are unsure of what to keep, you ultimately might have to decide to throw something out to make other loot fit. Which can bring up scenarios like: great I dumped my cure potions because I wanted to carry this spear, but now I'm poisoned and dying.
Finally, there is the stats side of the RPG, which is absolutely fundamental. My cleric doesn't have enough STR to equip this bp even though it would be great for her - what do I do. None of my characters have enough intelligence to tell if this item is cursed or uncursed or what the stats are on it, what should I do?
Many of these aspects, especially from the risk side of the scale, have greatly diminished over time. And you could continue to diminish them: why should I sell loot, loot should automatically sell. Yes, perhaps that is a good idea, but it also extremely changes the core gameplay of your game. However, as you remove gameplay, you also need to add gameplay somewhere else, by making some other aspect of your game more complex otherwise it becomes incredibly shallow. Bioware did this in Mass Effect with a really good story, however ME2 failed to hold my attention and is still on my unfinished games list. The story can only hold poorly executed gameplay together so long and the reality is that ME2 has little for me to play for.