Hobo Elf
Arcane
To be honest I wouldn't say Diablo 1 is really that much of a item farming game in the first place and many people didn't play it as such. Several of the "loot whore" items are single player only and not obtainable online except via hacks as you get them as quest rewards or drops from bosses with a 100% chance, and there are some unique items what we'd call cursed items i.e they are good but have some horrible negative side effects, which was dumped completely by Diablo 2. The game wasn't balanced in a way that you'd have to be decked out in the very best items to be viable. It wasn't until Diablo 2 when loot whoring became a real thing.