Well, to me a broken glass is not like a made like it one (as many small glasses strips side by side), you can have many glasses side by side with a small gap between them but a broken glass has broke from some shock, thermal or other and the glass can have a ""stress"" in it and may be dangereous to use. If it broke one time imagine if it breaks again from an other explosion?
As long as nothing happens all is OK, just like when you recommand to have a Co detector...but imagine if a glass blow out during night or when nobody at home...maybe $100 is expensive but some other things are much more than that. Who will be there if it happens and if the worst arrives?
By the way, all serious stoves manufactures recommand to stop burning a stove having a broken glass on it.
If a dealer would tell me there is no problem to keep on burning a stove having a broken glass on it, I would ask him to Write clearly that and sign it.