Usually when someone send files from his computer to his phone it is for sharing with others.
I own Nexus 5X phone. when my screen is locked receiving files will left me with nothing. there is no message/notification. On the other hand when the screen is on, the files would open depending on the default app which in my opinion a notification is a better way to interact with your files because then you can open it, share it or even add a delete option, depending on user choice.