Not really related to the original topic, but US carriers operating under Part 121 could NOT do that now if they wanted to. It's not allowed by the FARs. Jeppesen was pushing hard for many years to get that changed, but they seem to have given up (for now) after their last attempt.
I believe that it *is* allowed to outsource flight planning for 121 Supplemental rules (although they still need to have an in-house flight following system) but I'm not aware of any carriers that do so. I could be wrong since I've never worked in the supplemental ops/cargo field any.