Fur chewing can be for various of reasons, and can even become habit if the reason isn't solved quickly enough, like a person chewing their nails. The most common reasons are stress, boredom, pain, and genetic predisposition to fur chewing. Fur chewing, also called barbering, is not detrimental on it's own, so long as it's just fur not chewing creating sores. Also it's not that common but if they are swallowing the hair they can get a hairball that causes a gut blockage (they can't throw up), so something to watch for.
For the issues of stress and boredom they can generally be fixed by a change in environment to one that is more relaxed and offering more toys as well as more out of cage time and interaction. If it's caused by pain getting that sorted could help stop the chewing, generally with pain the continue chewing causing sores because they are trying to get rid of it. If it's become a habit or the chin is just generically a fur chewer you might have luck reducing it with distractions (toys, playtime, etc), but most will resort to it if things aren't perfect.
Yes, I would. Eye appeal is, of coursed, important, but it's more important that a chinchilla has a safe and happy home. I don't necessarily agree that fur chewing can be "cured" though as it can be genetic as well as environmental. And, as with any bad habit, once you start it's hard to stop.
Yes. In fact I actually brought 6 home, I wasn't happy with breeders very poor conditions. In fact I would go as far to say he's an animal hoarder. He had several hundred packed 3 to 4 chins in 10 inch by 18 inch cages stacked floor to ceiling, no hay, no stimulation, no clean water and dirty cages. All were barbering. I would have walked out with all of them if I were able to reasonably care for them, but I couldn't so I left with 6 and left it in the hands of the RSPCA. From the moment I brought them home they ceased to fur pull and now 6 months later they're beautiful furry clouds.