Q: Captive Bred vs Captive Hatched / Farmed

So I understand the difference, but I'm curious as to if Captive Hatched is to be avoided when buying a BP? If so, why?

I would take a captive bred over a captive hatched anyday.
a) Any captive bred is the descendant of a wild caught who survived the long trip over here, managed to switch from whatever native rodent to pet feeder mice/rats, and thrive well enough in captivity to bear young. Through natural (or unnatural) selection, it'll most probably be of hardier stock than whatever random wild parents of the eggs that were found.
b) Captive hatched are often hatched and then transported here; thus they will suffer from the long trip just like wild caughts. Also, a hatchery is less likely to take extra precautions against parasites or other diseases.

Not to mention, captive bred don't cost much more than captive hatched so I really see no reason why anyone would go with captive hatched.

Lots of people buy CH babies and do just fine with them. But you do need to go in with eyes open if you're considering doing that. If you buy them from a reputable breeder, you can mitigate a lot of those risks because the breeders will usually take care of the parasite issues and make sure it's feeding well before ever selling it. If you walk into a pet-store and buy one...you can almost count on having mites and internal parasites to deal with, as well as unknowns about feeding history, etc.