Indeed. The disaster at Rigel VII (which resulted in several injuries and deaths) was fresh on Pike's mind when The Cage took place. So that's most likely why he was so depressed. He feels responsible for the whole thing.
By the time DSC happens, he would have gotten over it. Back to the Pike he's supposed to be.
Burnham: It's a hundred light years to Starbase 1, we've got a full tank of dilithium crystals, half a pack of Starfleet field rations, it's dark on the bridge, and we're wearing Starfleet uniforms.
Pike: Hit it.