If we extrapolate then lets also do it for the impact of the disaster. Gen 3 disaster: nobody dies and nothing leaks outside the reactor containment vessel.

Your implication is that a reactor containment vessel in a Gen 3 nuclear reaction is capable of containing radioactive material no matter what physically happens to it (flooding, earthquake, asteroid impact, etc.) Is that accurate?

It's a rather facetious commentary on the "now it is gen 3's turn for a disaster comment", by implying that if that progression holds, the so too should the scale of damage.

The gen 1 disaster left land uninhabitable, the gen 2 disaster just took some cleanup, therefore the gen 3 disaster will be a non-issue.

Asteroid impact? Is the reaction even going to be critical at that point? Assuming you mean something smaller like a meteoroid, I think most US plants would either be okay, or you have other problems to worry about (like if any people are within multiple miles of the plant in every direction).

There would be an intermediate size asteroid that would be able to penetrate the containment and damage the core. That same size asteroid wouldn't be much of a worry if it just hit a field next to a town. On the other hand, that same asteroid could topple over some skyscraper and kill a few thousand people, which is more than the aforementioned nuclear-asteroid accident would.

I was just listing things that could affect the structure of the core. The real question about nuclear disasters isn't whether or not humanity can respond to them given functioning society, it's what happens when a society collapses (extended power outage, etc.) and then something affects the fissile material. Fukushima took a lot of people to clean up.

> asteroid impact

So at this point, we are concerned if the remains of people who would be killed by the asteroid, would also be slightly radioactive? An the 'remains' are being probably like finely pulverised ashes?

Like the containment building is basically a bunker, and the reactor vessel is like a thousand tons of steel. If any asteroid gets through that, the neighbourhood is already gone.

So many people pointed out Fukushima to me, and most of them did not know that the tsunami killed 10,000 people and radiation killed zero.

Fukushima was cleaned up by a massive task force using globalized technology. What I'm wondering about is if nuclear power is scaled to have hundreds or thousands of plants across the world, and something happens to humanity's ability to mount a globalized cleanup effort (using diesel, electricity, etc.), are the remaining societies safe from the effects of the decaying plants?

Fukushima was literally older than Chernobyl, commissioned a year before Chernobyl began construction (1972).

Age doesn't determine the design or it's safety. Soviet early designs had massive flaws, bugs and cost cutting measures to enable the fast deployment needed to keep up with Soviet energy demand growth, at significant risk.