What I thought was really great about D1 was that it was almost a coffe-break game. You could play if for hours, or only a brief amount of time. You could actually save your game - most diablolikes didn't have that feature.
You could reasonably hope to find any (or even all) of the unique items without having to play for a hundred years. It had a lot of loot that could drastically alter the way you play your character.
It had great art direction and good sound. Just a good game through and through in my book.
It was also fun to find stairs-down next to the level entrance, because you could skip the entire area easily and try your hand at a higher level area. A couple of skips like this and you would be happy to be able to lure & kill one monster at a time for a while, although I have to say going this far wasn't a good strategy as it meant you'd run out of HP potions pretty fast (at least as a warrior).
This genre is just really shitty and boring in itself, you know?
Nope, it just has to do a few things right:
1) Content that's easy to skip.
2) Properly reward exploring higher level areas as a 'thief' who tries to avoid monsters (higher level loot that you can use in chests).
3) Make that exploration challenging and make avoiding those monsters interesting/thrilling.
4) Properly reward managing to beat tough higher level enemies - possible to beat if you manage to find higher level equipment via above or other methods.
5) Make this higher level loot usable - no lvl restrictions on equipment.
6) Obviously no level scaling of any sort.
7) A monster level is just a sign of how badass the monster type is - no recycled skins or monster types except where solid lore allows it (Dragons).
8) Open world isn't a must but it's a plus.
9) Obviously the healing mechanic has to be well done - i.e. not allow defeating high level enemies without solid equipment or superb character customisation (except in rare cases where it's possible to lure a monster that's not too high level one at a time).
10) Great soundtrack.
11) Make all monster types kinda cool, the more so the higher level they are - no cases where you have cool low-level monsters but then level 20 slime balls or pygmies. No New Game+ bullshit.
12) Great sound effects.
13) Great gory visuals with a nice amount of variety.
14) A rather opaque skill and spell system that provide a couple of "over-powered" builds already near the beginning for those who manage to figure out the best ways to use them (Two Worlds has a good example).
15) Starting characters of somewhat different levels with not just different stats but different starting items & equipment that in some cases you can't immediately easily replace (an idea from Dark Souls games). This gives variety with regards to what you can do already when starting the game. With the right starting character, you could easily skip the first couple of levels for example. Two or so characters would have interesting items like Master Key from Dark Souls to help exploration and allow skipping content more easily.
16A) Hand crafted world like in Sacred 2.
16B) Secret chests, areas, etc. that aren't too easy to find and/or reward exploration.
17) Monster specific loot drop tables so you'll have to learn which monsters to grind-kill if you want certain drops. Loot system somewhere between Dark Souls (low drop rates) and Two Worlds (you always get armor from those wearing armor etc) - certain types of loot easy to figure out who drops and how often but others much rarer etc.
Still, I'd rather game developers started making Dark Souls clones. It's just that you're wrong that Diablo-clones can't be a pleasant enough time sink.