So first, you forget to mention:

1) a nuclear power plant that's in operation for ~10 years, then melts down releases less radiation than a coal power plant that's in operation for 10 years.

(another issue is that if somebody proposed the coal power plant solution, ie. take the waste, vaporize it and spread over a large area, that's apparently a bad enough offense to make the vatican consider an exception to their death penalty policy. And yet, every other form of centralized energy production DOES that. It would also be the safest option)

2) this obviously disregards all the other sources of pollution of said coal. CO2 is one, but that's just the tip of the iceberg. There's also Sulphur dioxide (which is directly toxic), the gigantic amounts of coal ash, liquid coal waste (preprocessing waste). I mean if you've ever visited a coal plant you would see that they are dirty, oily patches of ugliness where absolutely every plant utterly refuses to grow. You even have very very few weeds. Your lungs will tell you a mile from a coal plant something is very wrong with the environment here. Nuclear power plants, by contrast, are green oases : if you didn't know, you'd think it was a university garden or something.

(you could remark that that's because of Materials handling. Nuclear power plants handle a few hundred hermetically sealed barrels, whereas coal power plants handle megatons of toxic coal and -even more toxic- ash, which is just dumped somewhere on the grounds while in transit)

3) I want to make this a separate point, because it is. Nuclear waste goes out of the plant contained and controlled (except for the few hours/days that a meltdown lasts). In coal power plants, by contrast, normal operation is that a significant part of that waste gets vaporized into the atmosphere and hurts the surroundings (in actual, demonstrated hurt, not the typical nuclear "this tiny spill will end the world !" hurt. Sulphur dioxide especially is bad in this regard)

And lets not pretend that the remainder of coal waste gets handled responsibly. No, it is just dumped somewhere. It can't be any other way: there is just way too much of it to treat it like the nuclear waste is treated.

All of the top-25 "most polluted cities in the world", every last one, from last week's article on hacker news, is as polluted as it is because of coal power plants (not that cars don't make their contribution, but there's absolutely nothing that screws up the air like coal power plants. Nothing comes even close. Not even major goods transport highways)

4) And lastly, there's the mining pollution. Of course, nuclear has mining pollution as well, but coal mining, firstly, has worse pollution, secondly you need 3-4 orders of magnitude more coal mining than nuclear mining for the same amount of power (and 5-6 orders of magnitude more transport)

Second, we must not think about this in absolutes. This is the way the public opinion seems to work. We think in absolutes. In practice, of course, we need power, so you do not get to say simply "nuclear bad". In reality we have choices:

solar: pros ... cons ...

wind: pros ... cons ...

coal: pros ... cons ...

oil: pros ... cons ...

nuclear: pros ... cons ...

In such a comparison, nuclear is utterly unbeatable due to the energy density and lack of waste during normal operation. And I assure you, even wind and solar have hazardous waste when a disaster happens on a plant, so that's just another factor to be considered.

You cannot discuss nuclear power, or any form of power, without considering that it is but one of many options, none of which are perfect.

This stupid absolutist single-issue thinking is nothing short of a disease that is a dangerous obstacle to cohesive analysis and good outcomes.