>spread heavy metals
Like the trace amounts of Uranium in coal. And don't forget the Radon that comes up with natural gas either. For added fun, Radon is a noble gas so good luck economically removing it as opposed to just venting it all into the atmosphere.
The main concern are arsenic and mercury which accumulate in bottom feeding sea critters some of which we eat (mainly shellfish and shrimp). The uptake of uranium are thorium in marine species is rather low, but yes, burning coal also spreads radiation. Some of the byproducts of nuclear fission (I131, Sr90) are more dangerous because they tend to stick around in our bodies. Uranium and thorium get excreted but the first one is also toxic.
Of the two Radon isotopes, one has a half life of 55 seconds, the other 2.5 days. The main problem are its decay products: Pb210, Bi210 and Po210. It's better to vent it off into the atmosphere than to let it accumulate in mines and basements.
And burn coal instead, spread heavy metals and CO2 around and slowly poison everyone.
That is the alternative, we saw it in Japan after the Fukushima accident. Oh, btw, Tepco has announced it will discharge further nuclear contaminated water in the ocean as they ran out of space to store it.