Sadly deathknights feel nothing like necromancers at all. There is no flesh weaving, comanding of undead hordes or even noticable diffrent minions. Necromancers themself are rather weak and fill more a support role, while the minions do all the actual dps. DK's summon undead and the army are more tacked on token stuff for "look how necromancy-evil we are". Demo warlock is actually alot closer to necromancers in gameplay than death knights by a country mile.
You are right about the rest though. Bards simply don't fit the game because we have a holy trinity of tank, damage and heal and not tank, damage and support. And while shadowpriests feel nothing like they actually wield powers over the mind, that is mostly because for something like this you need context sensitive combat that would allow for more solutions than dps as hard as you can. Psionic would also only in name be about psychic stuff and feel just like shadow with another color at best.