Blade Ward is useful in a number of circumstances.
You've got Armor of Agathys up and want to stretch it further.
You're trying to defend against an invisible foe (Dodge doesn't work against foes you can't see), while other PCs do the killing with ranged attacks.
You're trying to defend against something with a monstrous to-hit bonus like an Iron Golem or a Tarrasque, and its damage is mostly physical. Other PCs do the killing with ranged attacks.
You've been restrained by a monster (Dodge doesn't work while your speed is zero) and are trying not to get killed while other PCs do the killing.
Additional twist on defense scenarios above: you're a multiclassed Eldritch Knight/full claster and you plan to use Blade Ward + War Magic Attack to set up for your spell next turn (perhaps Tasha's Hideous Laughter or Phantasmal Force of a larger and tougher-looking duplicate of yourself as a decoy), without losing a whole lot of HP in the process.