Why would you assume anyone aims for a carotid artery? With due respect, you obviously have no knowledge on the subject but make a lot of assumptions based on ...Anyone else impressed that TR hit his target, Kirk's carotid artery, from 200 yards out with one shot?
No reports that he is an expert level, damn good for an amateur or did he get lucky?

No shooter aims for a specific artery. Or the neck. It's like people asking why the cop didn't shoot the guy in the hand or foot instead of the chest.
A professional shooting such a powerful round as the 30.06 would aim for the chest, the centre of mass. The tissue and organ damage would be catastrophic and 100% lethal. Plus there is less chance of the target moving their head like Trump did.
The 30.06 is first (body) shot deadly against MOOSE out to 440 yards! It's only surpassed by 50 cal BMG and 300 Magnum/7mm Magnum.
BTW this shot was 120 yards. Any 12 year old can be quickly taught to reliably hit a head sized target with iron sights, no scope required.

But if a shooter is looking for a dramatic instagram worthy spectacle, the average non-pro is going to go for an exploding watermelon head shot. (Exception of police snipers who may go for the head shot of a hostage taker to reduce the risk of involuntary or last gasp gun discharge)
I've copied the YT link to start at the interesting part.