You really underestimate the paranoia involved in the system's design. We can't even connect the sub's Missile Control Computer to tge same sub's Radio Room, to make secure targeting updates idiot proof, because the decision people at SSP are so adamant about MCC being unhackable. Similar neasures surround the release codes in the isolated basement computers that generate and send them.
When they made the movie, Crimson Tide, the Navy updated the system by installing a safe that no one on board has the combination to.
Even if Eric Trump was somehow appointed CO of the Rhode Island, and Trump told him directly to launch nukes, he'd be physically incapable without the rest of the approval process agreeing to the justification for launch.
And those guys really want to avoid war crimes and their impact on post-service job prospects.
Yeah, "murdered a billion assorted foreigners" looks pretty bad on your permanent record; If it's followed up with "...leading to a retaliatory strike that killed 200 million Americans", you're really going to struggle to get an interview.
Even the GOP is unlikely to let you run with the "did they die of themonuclear bombardment, or did they have pre-existing consitions, and merely die with thermonuclear bombardment?" excuse.
Nah, they died by arson.