Nope.
Nuclear has an approx ~1% chance of blowing up during it's lifetime, rendering many thousands of km² unhabitable in the process.
Also it has a 100% of chance to poison the same ~1000km² during the next 10 000 Years.
That sounds really bad but what does it mean? What do you mean with "nuclear's lifetime", and how did you come up with 1%? What is the significance of "blowing up"?
The Chernobyl exclusion zone is 2600 km². Today it is basically a nature reserve with a flourishing wild life. It's not uninhabitable. It is preferable to not live there if you have the option since the increased radiation gives a (barely measurable) increase in cancer risk, mainly for children. Despite that, there are people living in the exclusion zone today who never left and they are doing just fine. The Chernobyl power plant continued to operate a long time after the accident, people went to work at "ground zero" every day for fourteen years. It's bad, but it's not nearly as bad as people make it seem.
It does not matter how often something blows up, the relevant question is how much damage per unit energy nuclear causes compared to coal (or water). The effects of the Chernobyl accident have been studied extensively so we know very well what the effects are. We also have a rough idea of how often they happen*. If you compare the numbers, coal is worse by a large margin.
* It's likely that accidents will be less frequent in the future since new reactor designs are inherently much safer. We learn from previous accidents which mean we can prevent the same thing happening again in the future. Nuclear isn't just safer than coal and water power, it will keep getting even more safe with time. On top of that, the medical science is moving forward and we are able to cure more and more types of cancer.
Coal doesn't do any of that, it only poisons a few km² around more reliably, and only for the few decades it runs(still bad)
Wrong.
Coal plants pollute the air and the air is spread around globally (or at least over the same hemisphere). The mercury in tuna comes from coal plants because the fallout from coal plants have poisoned the oceans. Ocean acidification is caused by sulphur dioxide from coal plants, it's what's killing the great barrier reef for example.
It's not possible to create a coal exclusion zone because it would mean that the entire planet would be made "uninhabitable". You are probably completely unaffected by any nuclear accident, but right now while you are reading this you are breathing in pollutants from coal power plants with every breath you take. You swallow it with every bite of tuna sandwich. The air pollution from coal is practically guaranteed to shorten your lifespan and lower your life quality. Conversely the negative effects from nuclear is zero as long as there is no accident, and if there is its effects are limited geographically and can often be mitigated.
If you check the data you see that we can have a nuclear accident of the Chernobyl magnitude every year and the health and environmental effects would still be less severe than those caused by coal power plants. (That takes into account that the radiation remains for a long time).
And we haven't even considered CO², the greenhouse effect and global warming yet...
and coal is in many cases the only alternative right now.
Nope.
Today, the most financially credible alternative is utility scale PV.
Except when it's cloudy, night or winter? Or what do you mean? What do you base that claim on?
Don't get me wrong, I love solar, we should use it as much as possible but it can't completely replace coal/nuclear yet. That is why the anti nuclear crowd don't say we can solve the climate change problem by using renewable only, instead anti nuclear people say we need to reduce our power consumption
a lot as well. Unfortunately they doesn't explain what we should do when the wind isn't blowing and the sun isn't shining. Sure we can survive without television but should we also just shut down the hospitals, the food production and the medicine factories? Do you believe the effects of doing that will be less serious than Chernobyl?
And sure, if they can make that happen, fine, but until then we should use nuclear to replace coal, gas and oil as quickly as possible.