You may not suddenly get sick from coal power plant smog but your life quality degrades over time and you develop certain diseases. Even though smog is a visible danger, nobody cares about inhaling it with a great cost to their lives.
There is only one nuclear accident (INES > 3) that has happened in the past 30 years and that is the Fukushima. On the other hand there has been 142 oil spill accidents in the last 30 years[1]. Several sources calculate that on average, cleanup of an oil spill costs around 5 billion dollars[2]. So, in short, oil spills has cost us 710 billion dollars to clean-up in the last 30 years, not including any health or repair etc. material costs. I would also be curious to find out a similar cost calculation for coal related cleanups.
New nuclear plants should not be built blindly. Japan perhaps should not use nuclear technology due to being in a highly active seismic region. But this should not stop other countries from investing in nuclear energy. For example, France is generating 71.7% of their electricity from nuclear sources and they are 'almost' accident-free.
[1] https://en.wikipedia.org/wiki/List_of_oil_spills [2] https://twnsacredtrust.ca/concerns/economic-cost-oil-spill/