If it is off it is off, no need to unplug every night.
We have our plugged into a surge protector power cord and we switch that off at night vs unplugging all the time (after shutting down the laptop) just because we don't use them again til evening and ours still has a good battery in it.

The battery is mainly for business people that need to have something portable and no cords to fiddle with.
Or people that want to move around the home or go outside with no cord..


You can try cleaning the contacts and see if it works or not, but you don't have to have a battery at all.

Plus the battery is a toxic thing to dispose of /or recycle when they do die.