Puggleman made a very good point. I've played many ARPG games from young till now. Certain monsters should be weak against certain element. I'm surprised that nobody mentioned it at all till now.They have. This isn't new.
The problem with introducing say... "Fire Immune" monsters is that certain classes that are dispositioned towards Fire would be at a SEVERE disadvantage. Believe it or not, this was a chief complaint in the Diablo 2 system - "the character I built is useless against Lightning/Fire/Magic immune mobs!"
So I agree from a tactical standpoint that it would be cool to have mobs immune or resistant to elements, but this isn't an element game. You can't freely choose your element. You just bought a 1400 dps 1h weapon that's Fire? Oh, so sorry, everything in Act 3 is immune to Fire! Joke's on you!!! lololol. In other RPGs, you can easily swap from Fire to Ice to Lightning at a button press. Here? Not so much.
So in the end; elemental resistant/immune monsters do not make sense for Diablo.
Easy. First, don't make mobs immune. Second, switch up the resistances so that not all mobs in one act/area are severely immune.
You are also forgetting that even resistant mobs should still suffer damage from melee dmg on the toon's weapon as well as melee based skill dmg. To even provide MORE depth, it would be a great way for classes to use under utilized skills/runes, as they would have to switch up their build depending on the enemy (what a crazy idea!). Also, if would provide greater use of gear as characters could even use, dare I say, more than one weapon while leveling/farming. That is, after all, one of the main reasons why characters could switch between weapons with the "W" hotkey.
If you don't like any of the above, there is another option that actually fits directly with the dev's vision of D3 as a more social game...play with a friend who does an different type of damage that compliments your build.
I don't understand why you pick an argument that limits the game so much. It's pretty obvious that if such changes were made in the game, that corresponding mechanics to work within the system would be implemented as well. Your example is actually a terrific example of a formal fallacy, "denying the antecedent" or "fallacy of the inverse"