Just came across this 2020 study comparing cruciate tear surgeries versus conservative management:

Disease-related and overall survival in dogs with cranial cruciate ligament disease, a historical cohort study

Conclusion

Disease-related euthanasia due to CCLD was not uncommon in this population of dogs, which shows that CCLD can affect life expectancy. Both treatment strategy and variables related to signalment and history of the dog were identified as risk factors for death/euthanasia. Surgically treated dogs had a lower hazard compared to conservatively treated dogs, which is in concordance with our hypothesis. In addition, comorbidity and increasing age and weight increased the hazard. Information regarding life expectancy in relation to risk factors is valuable facing a decision about treatment of CCLD.

Essentially, the surgeons found that dogs with no comorbidities (of which being an amputee would be one), who were treated with surgery lived a longer life with better quality of life than dogs who were treated with conservative management. Dogs in the second group met earlier deaths mainly due to mobility problems. 

This study coincides with one done specifically about amputee dogs who had orthopedic leg surgeries. It was published a few years ago at Colorado State University. The Postamputation Orthopedic Surgery in Canine Amputees Study showed that post-amputation surgeries resulted in high owner satisfaction rates. 

Another article about conservative management for soft tissue injuries:

How Do I Treat Soft Tissue Injuries in Pets?

https://vitalve.....es-in-pets