Hello, having a locked backround layer is done by default, so that the image could be saved in the same format.
I would create an action that converts the background into a layer, then run it via the Script Event Manager.
Open one image with a locked background.
Show the Actions Panel (Alt+F9)
Create a new action set (click on the folder icon, name it for instance "Auto")
Create a new action (Click on the [+] icon, name it for instance "Auto Unlock")
Double-click on the background layer, click OK (name it if you want)
Hit the stop button (the square in the Actions Panel)
You might want to select the Action set, and go to the flyout menu, and save the action in case you want it on another install/version.
Go to File>Scripts>Script Events Manager
Check Enable Events to Run Scripts/Actions.
Select in Photoshop Event: Open Document
Click the radio Button in Front of Action: [your set, for instance Auto] [Your action, for instance "Auto Unlock"]
Click Add, then Done.
Now, each time you open an image, it will convert its background into a layer, unless you go to the SEM to disable it.
(lol, all this was typed at the same time the others replied)