Modern designs have greatly expanded the passive safety features of nuclear plants. In the new Gen III+ reactors this accident would not even have been possible.
That's well and good, but there are hundreds of reactors operating now that are going on 50 years old. Old equipment and containment buildings can fail more readily, pipes can leak or burst, a cooling water supply could dry up in a drought, backup generators could go down, or maybe something else nobody thought was possible actually happens. Whenever the fit hits the shan, the world has yet another huge problem.
With a major meltdown/radiation release happening every 20 years or so on average (plus all the little leaks where they assure us "there is no danger to public safety"), they really don't have a very good track record as a whole. They're ticking time bombs. Most of them have served us well, but now they need to be phased out ASAP.
I'd rather see their output replaced by as much wind and photovoltaic as can be manufactured, but newer passively safe (we hope) reactors probably will also have to be part of the picture. That still doesn't answer the question of how to safely deal with waste fuel, so the stuff will continue to pile up, but as has been said: pick your poison.
IMO, it's too, too, too risky to keep operating inherently dangerous reactors indefinitely, so if we MUST do nuclear, lets minimize the risks and start getting rid of 40+ year old reactors right away. I really don't care what it costs, because the cost of NOT doing it is too great. Apparently, a vast majority the Japanese population feels the same way, and I can't blame them one bit.