I want the game to have a story to keep me playing, and the loot should represent the things I need to keep progressing through the story. If they become the focus of the game, it's broken.

You need a better set of equipment from time to time, and the game needs to give you that either directly, as loot you can use, or indirectly, as stuff you can sell in order to buy what you need. The quests that provide information, or entry to another quest are more important to me than the ones that give me an overpriced lump that I won't use, and can't sell for its marked "value". My Oblivion characters typically use equipment they've enchanted themselves, using base items bought from vendors. They need to find loot to sell as they go along, but it doesn't have to be epic, or even useful beyond its sale value (by which I mean the gold I can get by selling it, not the price on the tag). Most of my dungeon-diving is done for weapon or spell practice, and I frequently ignore the chests unless I'm running short of cash, and even then it's often easier just to make and sell a few potions.

I'd be happy if there was no "loot" in dungeons at all.

YES! But let them be non-quest related. Like a quest with no journal things or stuff like that. Morrowind had some stuff like that, and I loved it! If Oblivion had it, it didn't make a big impression, because I certainly don't remember it.

In Morrowind however, I remembering there were tombs were a skeleton was. And you could read their letters talking about some treasure or something like that, how they tried to get it but failed. And when you read that, you knew there was something nice ahead of you... but with dangers. It added such a big and cool atmosphere and I loved it!

I agree as well, add more unique rare items to make your time and success rewarding. It could even be a map that say, shows a hidden cave with ice/snow covering the entrance that you could then melt or hack to get inside to fight your way again through more creatures and find a valuable item.....or maybe even another map leading to yet another place......and maybe after that yet another map revealing a hidden area in the very first dungeon you went through that if you stubbornly stuck with this chain of maps end up with some uber weapon, etc.