Why do you say Sallallahu Alaihi Wasallam after the Holy Prophet’s name? We say because it’s a form of praying for him to evoke, invoke Allah’s blessing upon him because he did so much for us. Out of all those who were benefactors of mankind, he’s the greatest of benefactors. As somebody who treats you with favour, it is quite natural for you to thank him, even to do something in return, to do some service.
We can’t do anything for him in return for the immense favour he has shown to us by living a model, living a life of sacrifice, by being so good as the Holy Qur’an was revealed to him which contains so much of wisdom for us and light for us, so we owe him something. The least we can do is to pray for him whenever his name comes, right?