Modernizing nuclear power plants will not address the management rot that I believe is ultimately more harmful than aging plants. Just my 2 cents.
Yes there are problems. I think they can be overcome with oversight and innovation.
Its sadly ironic that the fight to eliminate nuclear energy has made the plants less safe and more likely for accidents. Its stifled innovation, prevented safety from being added to existing plants, force obsolete plants to continue operation, and prevented good people from entering the field.