We used to call this "pushing your luck" during my motorcycle days. Front brake failure? It's OK, I still have a rear brake (at the moment). Engine running lean? No problem, I'll just "ride it out" if it seizes up on me at 50+ mph. Tire worn bald? It's OK, my riding skills will "make up" for it... Like the saying goes; there are old riders and there are bold riders. But there just aren't many old bold riders.
Knowingly and willingly riding a machine when you know that a structural and/or other critical component has been damaged isn't a good idea imo. It just a matter of common sense. And again, please don't give me the foolish "my skills are such that I can "ride-out" most any break-down (truly skilled and knowledgeable riders don't take unnecessary chances with questionable equipment).
Sure, "new things break", but why would you both knowingly and willingly risk riding a damaged bicycle? Limp the thing home? Maybe. Continue to ride a damaged bike when you have family members that rely on you? Not a good idea imo.