Commercial nuclear power is the only major U.S. industry that was not born out of the desire to make a profit. The first nuclear power plants were designed by government and academic engineers with no regard for how much the plants would cost, and every regard for the safety of the public. Every nuclear power plant goes through constant checking and testing, both according to internal and government rules and regulations. The "state of the art" in nuclear power plants is constantly evolving to be safer than before.
The events of Fukushima and the way that plant went down were a "perfect storm" of poor site selection, the juxtaposition of extraordinarily rare events, and the least safe design (GE-BWR) in the western world. It COULD NOT HAVE HAPPENED anywhere in the U.S. or western Europe.
The non-problem of storage of spend fuel (aka "nuclear waste") can be laid squarely at the feet of Harry Reid. Look it up. Yucca Mountain.
Don;t forget Jimmy Carter stopping the reprocessing of spent fuel rods...done elsewhere, reduces waste by about 70%.