All of the problems with nuclear reactors have happened to plants which were designed and constructed in the 1950->1970s. As it turns out, we've learned a ton about safely operating nuclear plants. The problem is upgrading these old plants rarely happens and getting newer plants to replace them is equally daunting.
There are 3 examples of major nuclear plant problems. That doesn't seem like too many.
In contrast, there are hundreds of operating plants. The newer ones are particularly safe because they require positive input to keep the nuclear reaction going. Any sort of earthquake, tsunami, mudslide, etc that causes the plant systems to fail will cause the nuclear reaction to be halted.
Chernobyl, 3 mile island, and fukushima are all impossible in plants built in the last 25 years. (Gen III or newer)
I support research and trials of the SMRs, but you might want to consider the possibility that it really is hard at the full-system level. The human mind does not readily understand invisible, exponential process like radiation.
A statistic that only works because epidemiological studies into the long term effects of radiation exposure are extremely difficult, complex and time consuming.
Something made even more difficult by the fact that we blasted uranium fallout in the atmosphere that's hanging around to this day, so getting a non-affected control group has become pretty much impossible.
Ain't helping that any research attempting to investigate the problem will very quickly be labeled as highly controversial by pro-nuclear lobbies [0]
By comparison, atmospheric nuclear tests added 0.11 mSv at their peak in 1963, declining to 0.005 mSv/year today. Chernobyl added 0.04 mSv in 1986, declining to 0.002 today. The nuclear fuel cycle adds 0.0002 to the global average, and is required to be less than 1 mSv for all members of the public.
The highest natural background radiation is in Ramsar, Iran, with 6.0 mSv/year. Studies are ongoing but the evidence so far shows no negative health effects.
Note that Sieverts are normalized to the health effects on the human body. Any concerns about different types of radioactivity are already accounted for in this measurement.
Chernobyl and Fukushima of course caused larger exposures to nearby inhabitants, and these exposures are accounted for in the statistics I mentioned.
Is nuclear really safer than solar?
This[1] has some data and estimations for death rates measured based on deaths from accidents and air pollution per terawatt-hour (TWh), which suggests nuclear has 0.07 deaths per TWh, which is marginally higher than wind (0.04), hydro (0.02), and solar (0.02).
So, it's very close!
The larger deployment of utility-scale solar does seem to have reduced it's death rate. (Many of the solar deaths are from falling off the roof during installation or maintenance. Utility-scale solar is normally on the ground and with better safety measures.)
I think this is fair. /All/ deaths from nuclear and renewable power are due to accidents and bad decisions. Accidents and bad decisions aren't going to go away. It takes a monumentally boneheaded decision to make a nuclear power plant dangerous, but apparently the rate of monumentally boneheaded decisions is one per thirty years at our current level of nuclear power usage.
That rate is very likely to increase as time goes on and reactors become older and thus more prone to failure/some freak low probability incident happening.
The NRC uses a value of $9M for the value of a statistical life. That is, it is worth spending $9M if that will save one expected life.
Nuclear, solar and wind have deaths/energy somewhere in the ballpark of 1 life per 10^10 kWh. So, at $9M/life this cost is roughly $0.001/kWh. This is very small, which says that even minor differences in the cost of energy from various sources will be more important than the direct number of lives lost.
(This would not be true of fossil fuels, though.)
TLDR: it's more important to reduce the cost of energy from these non-fossil sources, and to choose the sources with lowest cost, than it is to make them safer. For nuclear, inherent safety could be useful if it would enable cost to be reduced, but not because nuclear needs to be safer.
This one is particularly interesting considering Fukushima wasn't the first time something like that happened. On the other side of Japan is the Kahiwazaki-Kariwa plant [0], the largest of its kind on the planet.
In 2007 that plant was already hit by an earthquake, shaking the plant beyond design basis, it was shut down for 21 months after that.
And even tho it wasn't affected by the 2011 earthquake that blew Fukushima up, it still was shut down to implement safety improvements, it remains shut down to this day with no date for resuming operations.
[0] https://en.wikipedia.org/wiki/Kashiwazaki-Kariwa_Nuclear_Pow...