Oh man, I wonder if there's more to tanks than just Tankiness and Damage.
Could you possibly give more examples? Like, a lot of Juggernauts, Darius and Illaoi in particular, their stats are a good side effect of gameplay. Their surplus healing comes from hitting wonky abilities, Darius needs to build up his passive, Illaoi needs to stack her E or Ult.
A lot of Dive Fighters also do need to choose between both. Take a Hecarim or a Vi or a Shyvana and, all else being equal, they're all rather squishy early game before they can build defensive items and they can never truly match a Tank because they need offensive items early to make it to the mid game.
There aren't too many champions that get both that aren't also terribly designed or really old (Mundo is both, for example).