To pick an example, this green bean canning recipe gives the same processing times for both hot and raw pack. Presumably even with raw pack, the 20-25 minute processing time is enough to thoroughly cook the beans. Why would you cook them additionally first? Is it just for people who like very well-cooked vegetables?
According to Pick Your Own, the main reason is that in raw packing, more air is introduced into the jar. This may lead to discoloration over time, which is an aesthetic issue, rather than a safety issue.
Regarding hot packing, they describe the benefits:
They provide the following guidelines regarding which method to use:
See also: National Center for Home Preservation describing the differences, benefits, and reasoning in great detail.