For example does disintegrate benefit from +% chance to shock/burn from items in any way? Like on a per second basis, or is there no effect?
Since they’re almost always “on hit”, no, Disintegrate wouldn’t benefit from them. Sometimes a channelled/duration/DoT skill will have a node that applies a % of your on hit effects each second. Such as Disintegrate’s “Dragon Tongue” node. Or there can be uniques that allow that to happen such as Sanquine Hoard.
Some things don’t specify that it’s on hit. Ceraunomancer from sorcerer passive just says “+ shock chance with lightning skills.” There are other instances too.
True, but I think they’re coded as “on hit”.