If this feature exists, let me know, but I looked for it without finding it.
On occasion, I've left my PS4 controller connected to Input Mapper after finishing playing a game, and forgotten to turn it off. And the controller ended up running while connected for some hours before I noticed that its light was still on.
The Xbox controllers automatically turn off after, I think 10 or 15 minutes of inactivity, and it would be great to have a setting in Input Mapper to disconnect a connected controller automatically after a set number of minutes. The number of minutes could also be customizeable, which would be neat.
Since an empty lithium battery kills the battery capacity, it wouldn't be a good situation for the PS4's lithium battery if a connected controller wasn't turned off, and it ran until the battery was drained, and then sat unused for a couple of weeks.