Problems how often and how sever are a design issue. In current Gen IV you have GFR's that use helium as a coolant, it floats and is unable to stay radioactive for long, Compare to a Gen II with water it stays radioactive for a long time. Gen IV plants can use previous gens waste as fuel, some of the design are fairly proliferation resistant and that is a HUGE issue with helping the third world skip the industrial use of fossil fuels for power and heat.
The point is we got stuck on gen II plants, Gen III has come and gone and were just starting to see ground broke on gen IV plants.
Insurance is about the hype, fact is you get more exposure being downwind from a coal plant sure people are scared but thats because others told them to be.