Esthetic component of the final restorations - crowns or bridges is part of an overall success. Modern techniques and materials allow to create natural look for the crowns. It usually takes art for a team of dentist and lab technician to create the restorations that will look like natural teeth. And if the patient is unhappy with existing crowns and bridges it is reasonable to change them. 10 unit bridge with 4 abutment teeth seem like a questionable construction, due to too many teeth, too little support. Fixed crown and bridge work on teeth can be long-term solution in multiple cases which was supported by various research. And the long-term research show that 2 teeth can not effectively handle the occlusal load for 5 teeth without changes in periodontal ligaments and surrounding bone. Long term prognosis is optimal for 2 strong abutment teeth that can have a load for 1 pontic. Abutment teeth will start suffer at some point and loose periodontal and bone support, get mobility.
So, before you will consider changing the existing bridge your dentist will re-evaluate current condition of abutment teeth and probably alter the type of final prosthesis. After removal of old restorations patient will have the provisional crowns or bridges till the end of the treatment. Usually in big practices (prosthodontic, general dentistry) metal from old restorations is collected and send to one of the companies which utilize it.
You can try to contact with one of these companies and sell it yourself, but you will be surprised how little it will cost. Most optimal metal for crown and bridge is high-noble with high content of gold and platinum. The metal from previous restoration is not used for the new one because it has to be absolutely free of any oxides that occur from baking the porcelain on top of it and after many years being in the mouth.