You also have to "read the tea leaves". I can see a case where there is one, lone Trad family member, in a sea of novus ordo-ites and the Trad asks the dying person if they want a Trad priest. The dying person says "no, I want Fr Bob from down the street."
At that point, it's a waste of any Trad priest's time (and also a deception, although for good intentions) to call a Trad priest down to a hospital, only for him to get turned away.
Probably what happens more often is the Trad doesn't even ask the dying person if they want a Trad priest (because they know the answer) and calls one anyway. The result is the same - the priest is turned way.
If there were hundreds of priests in each state of the US, ok, no problem. They have time. But calling a Trad priest for an openly anti-Trad or anti-religious person, in this day and age, is a waste of time.
It's a different story if the dying person is open to conversation; but most aren't. That's reality.