Very true, although he doesn’t show remorse at all after they leave the farm. He also seems only briefly upset about Obi-wan. Possibly just straightforward characterization, possibly just how the hero is written in this genre. Even Leia just says ‘we have no time for our sorrows’ before the final battle and moves on. Then again perhaps this is better than these days when every lead has to be full of trauma and regret.
My interpretation is that he inherited a natural tendency to go cold when experiencing extremely vulnerable emotion from his father. It’s one of the ways the ESB reveal adds a layer to SW77. Tendencies in emotional regulation have a genetic component.
The difference between father and son is that Luke then allows himself to feel and then lets go, so he gets to remain that warm hero we know and love. Vader doesn’t, so he remains stoic.
The people who go cold are actually the most sensitive, because they’re too sides of the same coin. I relate to that deeply with my ADHD.