Are There Cases Where Braces Are Not an Option?

First of all, I am glad you said "Dentures are not an option".  Your question is difficult to answer without actually seeing you to evaluate your teeth.  Having said that, I can't imagine that something couldn't be worked out to straighten your teeth.  It may require minimizing the time in braces by using removable "Dentofacial Orthopedic" treatment appliances prior to braces.  These removable appliances, originally developed in Europe, can create new bone structure prior to braces.  This shortens the time in braces by as much as 50% and eliminates the need for removal of permanent teeth.  Look at my before and after cases to see more of what Dentofacial Orthopedics can do.  An evaluation and 2nd opinion could provide the answer.

Braces depend on adequate healthy tooth structure to bond brackets.  If teeth are not healthy enough for this, then crown/veneer treatment is likely needed to prevent tooth loss.  If they are not healthy enough for THAT, then extractions likely are needed.  This would likely result in dentures or implant supported crowns and bridgework.

Without complete diagnostic records it is impossible to say what would be best for you or even possible.  Many have been shocked at what COULD be done for them and the amazing results at the end, so possibilities are varied.