That's an interesting article. But no fighter-jet will ever be useful at stopping an ICBM once it hits Mach10+.
It seems like the F35 anti-nuke idea is to fly the F35 into enemy territory, and then shoot down the missile _BEFORE_ it reaches those speeds. I don't know what kind of situation would give us advance-warning of a nuclear launch, enough time for F35 to scramble into North Korea (violating the DMZ) and then effectively shooting down an ICBM before it reaches top speed, but... hey... weirder things have happened.
Weird contingency plans are basically the military's job. Maybe the situation will come up. Or maybe that situation is aimed for some other nuclear-armed country with a space program (China, Russia?)
What about something like this rather old https://en.wikipedia.org/wiki/ASM-135_ASAT ? There should be some updates meanwhile. Anyway. Assuming NORAD or similar has the rough ballistic track of the potential intruder, and can thus determine the entry ellipsoid, why wouldn't some jets on air patrol in or around that ellipsoid be capable of intercepting it with an air launched system?
As I understand it in my utter ignorance, you don't have to race with something coming in and down at Mach 10, or more. You just have to be in its way at the right time. Which seems doable, in this case, coming from NK, high over the Pacific.
Given the amount of infrastructure modern air forces require, it doesn't matter if the jet is alive and well in the air if all of the supporting cast is incinerated.
Good point. Although, if there's any chance of these difficult to replace assets surviving you'd probably want to take it. Any local airfield with a strip just barely long enough would do.
Deterrence from opportunistic attacks by other parties is also something that comes to mind, but I'm not sure if that makes any sense in these scenarios.
https://futurism.com/military-f35-nuclear-missiles