To your first part:

What happens if a pilot becomes incapacitated on one of these quasi-drones and how are breaks in the link to the ground monitor handled?

To your second part:

Is the cost of training still the same? Is the responsibility to the folks in back or on the ground any less? Have the inherent dangers been lessened? Are we spending any less time away from home?

Not really advocating for or against. These are questions that have to be answered before this type of situation goes live. Of course we all want there to always be 2 people up front though.

It'll happen gradually at first.
Cargo will have single pilot ops on heavier aircraft first, then acting as a backup to the advanced automation.
Once a quantifiable improvement in economics and safety is proven, the passenger sector will follow suit.
Unmanned cargo planes will be next, likely on trans pacific and or trans atlantic routes between large hubs with half of the airport dedicated to unmanned ops.

An intermediary with heavy single pilot ops would be a ground controller responsible for a group of airplanes or a sector. This person would act as a helpdesk for airplanes in distress by checking airplane vitals, assisting communication, and setting up navigation during an emergency. This will evolve to controlling multiple heavy UAV and single pilot assist over time.

So why not now? The laws and procedures need to catch up with the technology. See and avoid technologies need to be perfected, and ground procedures also need to be refined. It will also require greatly restricting general aviation in high traffic areas.

We are basically waiting on an "over the hump" moment. The instant it becomes legal AND economically viable, it will happen quick. The pebble that starts the avalanche is difficult to predict, but a pilot shortage could be one of those triggers.

So to answer the initial question: "When will pilots become extinct?"
Never, we still have horses and riders, they are not the dominant transportation species anymore. The pilot position will decline.

Some will say that the avalanche has already started.
It's too late for the pebbles to vote.

I'd say its somewhat comparable to supersonic flight. Is it possible? sure? Is it safe? Most of the time. Is it financially suitable? Not at this point in time. The airline industry will need computers that can think critically like humans before they remove them from the cockpit.

i don't want critical thinking, I want logical thinking.
10 years ago I saw programs that would land an airplane with multiple system failures using novel solutions. Combine that with modern AI and you have a practical solution.

We had to wait for Tesla to cause an Avalanche in the automotive and solar industry.

Who's turn is it now?

There is no such thing as AI, at least not the way the average person tosses the term around (HAL 2000).

There are programs which can execute complex decision making, assuming ALL of the factors are pre-defined in the code. The benefit of something like this is to replace low-skilled labor such as an IT help desk. That labor is reading from a script for the most part, not exercising creativity or judgement.

There are some programs which have the ability to learn but they learn from experience.

Software has no ability to utilize imagination or creativity to predict possible outcomes when confronted with an unknown or uncertain situation. This could be something like a UAL 232 event, but is much more common on a routine basis n the form of weather or in-flight delays.

In that scenario, best case, the software reverts to safe mode which would be an abort or divert. Not economical to do that on a regular basis.

Worst case, everybody dies (except the AI, which can restored from a backup copy).

Really?!!! You don't want critical thinking? Hope your'e not a pilot...

You don't understand AI, and that's ok
And the programming I referred to was specifically tested on a United 232 scenario and was successful.

It's just thinking. Period.

Somehow it became trendy to try to bloviate the concept into an expanded analysis of thought, with "critical thinking" being a popular college concept to suggest a higher, more advanced way of thinking.

Bull****.

It's just thought.

We're not paid for our monkey skills. We're paid for our judgement.

Sure, but there's a difference between thinking and critical thinking.