For years Balsa was the least expensive core material. That made it the most used and also the most miss-used core material. There were many poor building practices such as not adequately wetting out the core, walking on the core after it has been put in place, not keeping packaging sealed which allowed moisture content to increase and so on. Moisture in the core retards the time it takes resin to gel and also affects the cure rate. Resin drains from the inner skin leaving pockets of styrene gas. Walking on the core leaves pockets on the outer skin. Not only do you have poor bond, but also the resin around those pockets will not cure.
While a lot of people blame water ingress into core on poorly bedded through hulls or unsealed screws, the fact is that if water is present in the bilge, the summer heat will turn the inside of a boat into a high humidity environment. While water may not pass through laminate, water vapor quite easily does. Proper infusion fills all the kerfs in a core, but early infusion attempts often left a dry porous laminate on each side of the core..
Polyurethane foam is not a suitable structural material, it is only suitable for flotation. Both linear and cross linked PVC as well as Linear SAN foams are good structural materials provided that a density (sheer strength is directly tied to density) appropriate for the application is chosen. When PVC density approaches that of end grain balsa, so does it's sheer strength.
In order to support rot you need moisture, air, and bacteria. Those three elements do not exist together in a properly engineered and built laminate. Rot only exists where the laminate has failed and allows these elements to enter. i had test panels out in the weather for 5 years and checked them every few months. Rot developed along the exposed edges of the panels, but did not ever travel more than a half inch away from the edges.
The good thing for people buying used boats is that most problems with core show up within the first couple years. They will have either been fixed or should be easily detected by a competent surveyor.