The same thing happened to me. I ended up fine and in my case I didn't even end up needing braces due to the extraction (I only had four -- a whole set removed, though, so it is probably different for your granddaughter). I now have a perfect smile.
If crowding is the cause of her problems, you might be risking cavities in very difficult to treat spots by waiting.
The only side effect I've read about (out of curiosity) is that it may reduce upper lip protrusion by a couple of millimeters, giving a "flatter" look, but if she needs that many teeth removed that may be a desired side effect in the first place. It’s 15 years later and I still have large kid cheeks and I *wish* it'd sunk in my cheekbone structure as much as random people on the Internet claim the procedure does.
When I got my teeth pulled I just kept my eyes closed and listened to music; it's more comfortable that way. She will not be seeing her own blood, even with her eyes open (unless she looks right when the tooth comes out) and with the novacaine she probably won't even taste it. The sound is more terrifying than anything else, so definitely prepare a CD player, portable radio, or MP3 player. Anything really.
Listen to the experts because this really is a case by case thing that random people on the Internet can't advise you on and get a second/third opinion if you really aren't sure.
As for anti-amalgam dentists and unnecessary root canals? Yeah, stay the heck away.