this may be an unpopular opinion but viewing trautman and rambo solely through the typical "father and son" lens and leaving it at that is reductive and sanitizes a lot of the moral complexity in their relationship and the central message of first blood in general while also absolving trautman of his role in rambo's exploitation. i'm not saying that a father and son angle does not exist, it most certainly does, but it's undoubtedly the angle that's the least focused on in FB.
trautman does care about rambo, but FB also goes out of its way to emphasize the power imbalance in their relationship (trautman is a career military man, deeply respected, and neurotypical. rambo is basically just a grunt [he did serve in a specialized unit, but the people back home don't know that and treat rambo as any other soldier/vet], he has no power in civilized society as a homeless man with no capital [made more complicated by rambo being canonically indigenous, though i understand if a lot of people treat rambo as functionally white because of the racial implications of an indigenous man being played by a white actor], and he's mentally ill), trautman speaks of rambo fondly but also dehumanizes him and talks about rambo as though he's little more than a weapon owned and made by trautman ("god didn't make rambo, i made him", teasle describes rambo as "one of trautman's machines", trautman occasionally addresses rambo as you would a child: "look john, we can't have you running around out there killing friendly civilians.").
to him, rambo's value comes from the fact that he is such a good soldier. trautman's ire for teasle and the hope police department doesn't come from their brutality generally, but the fact that their brutality is directed toward such a good soldier ("that's gonna look real good on his grave stone in arlington: here lies john rambo, winner of the congressional medal of honor, survivor of countless incursions behind enemy lines. killed for vagrancy in jerkwater, usa.").
erasing this colder side of trautman really hampers the source of first blood's drama and tragedy, that rambo essentially has nobody in his corner. teasle and the police department is the america that neglects and spits on its veterans, trautman is the unfeeling government that both abandons and uses vets for their own political capital. rambo crying in trautman's arms at the end of the film is less a son returning to his father and more a man with nothing left to lose returning to a devil he knows, and what better a devil than the US government?
