I'm no expert on classic/vanilla, but from what I've gathered a traditional trinity setup seems ideal for dungeon clearing. Personally I would go for a mixture of armor types as well since personal loot is not a thing as to minimize the amount of pointless loot drops, but that's down to preference.

You are correct in that, in general, when you add more classes, roles and specs, you either increase how much you need to rely on your setup and/or how much micro management is required to get the most out of your team. However, I don't think a fully mixed team is not going to be achievable in classic. Some classes like rogues and ferals are probably problematic to work with, but others might be just fine. Again, I never played vanilla so I'm not 100% certain as to how rotations were then compared to today. What I think it comes down to is finding the right balance between efficiency, utility and fun for you,