Do you keep always the battery on the laptop
Well, I tend to keep my batteries
in the laptop, rather than
on . Most batteries are not exactly works of art.
Back to the question, and with a big fat DISCLAIMER that I am NOT a battery expert, I would say the following :
(1) Modern batteries are designed to work on a top-up charge basis. The old days of it being a good idea to run your battery flat before recharging in order to "condition" it are long gone.
(2) Laptops have fancy PMU (Power Management Unit) circuits inside them that take care of the health of the battery and when it needs charging. When you plug your power cable into the laptop it doesn't feed straight into the battery, it all goes via the PMU.
(3) I suppose leaving the battery out could also affect the thermal design of the laptop and so put thermal stresses on other parts of the laptop internals that would not normally be subjected to them if the battery was in place.