I can't agree anymore wholheartedly than with your deduction. Another important role of nuclear power is the zero emmisons of greenhouse gasses and the fact global warming would be alot farther along right now if it wasn't for the over 400 reactors worldwide that have been operating for decades.
Most power plants are coal and burning and coal releases significantly more times radiation than would ever be considered allowable from a nuclear reactor. Coal has uranium in it and releases it along with sulfur dioxide, nitrogen oxide, carbon dioxide in the millions of tons with vaporized mercury, arsenic, thorium and other heavy metals. This potent cocktail of gases, radiation and dangerous metals is pumped into our atmosphere by the hundreds of thousands of tons day in and day out. This does not include millions of tons of toxic ash are hauled away and must be buried with consequences yet to be realized.
Nuclear reactors produce very little waste and this waste is safely contained until a solution is decided upon. Most everything else we are using for power is contaminating the air, water and soil and has be doingso for multi-decades.
Nuclear is a no brainer and once the masses become educated and lose the medi-instilled fear of nuclear power we can all look forward to brighter future. I have yet to see a legitimate argument against it when faced with our existing energy and global warming problems.