It's (very roughly) ~4% gammas; the rest is easily shielded betas. We know this because they went into the basements of reactor 2 and 3 and we know how long they stayed, what their measured radiation dose was and what the dose-rate measured just above the water surface was.

The dose-rate just above the water is 10300 mSv/hr. But the dose rate to a person, if they are foolish enough to go in there, is ~400 mSv/hr with decent, water-tight protective clothing.

With a world of 15 billion people powered exclusively by nuclear power, over 200,000 new nuclear reactors would need to be constructed.

Thats ten times the current energy consumption, and unfounded assumption. 20 000 reactors is enough to power todays world.

One could expect a melt down similar to this one once every few days.

Nope, because new reactors are designed to be much safer. So that is another unfounded assumption. In reality, it is naive to try to statistically predict what would happen in such nuclear powered world.

/me gets a few dozen Luminal pills. If nothing bad happens, great. First great meltdown that inundates my country in a lethal dose of radio-isotopes, I am outa here.