Review those designs and accident reports. Two too many failures; but, they could have been mitigated.
Graphite moderated reactors were considered too dangerous for commercial use by the late '50's or early '60's by every country except the U.S.S.R. It was cheap and they needed power so they built quite a few of them. It is difficult to know exactly what happened; but, it appears an ill advised and unauthorized experiment was run on the system, with all the safeties turned off. When the reactor crashed, the operator(s) panicked and they tried to do something which was known to cause explosive power surges which could result in catastrophic failures. And it did. This should not have happened.
Fukushima Diachi was a 1960's design that is considered quite dated and had a few known failure modes. The company operating the reactors basically refused to do all the expensive updates to improve the reactor's safety. They also ignored warnings that the sea wall was inadequate for worst case tsunami, which happened. It flooded their electrical system(s) and generators, which were at or below grade level. Because the earthquake knocked out their grid power supply, they had zero options for power. This led to the loss of cooling. Then, for political reasons, the operator tried to downplay the damage, rather than ask for help when they desperately needed it. It did not have to be this way.
Frankly, with the aging inventory of reactor systems operating in the world, I do not expect these to be the last. Having said that, for the purposed of full disclosure, I live near two large power reactors, a major naval base, and one of the two shipyards where they build, overhaul and test nuclear powered ships in the U.S. I don't fear it.
Waste storage is something we do need to solve. Either through re-use or through deep storage somewhere. I don't have an answer for you that's based on real engineering.
"Spock, did you see the looks on their faces?" "Yes, Captain, a sort of vacant contentment."