In modern devices (mobile phones, tablets, laptops) the battery charging current is automatically switched off when the battery reaches 100 %. After being disconnected, the power supply cools down. It is a healthy practice for the battery.
But if (after the charge) the device is kept connected to the mains and is used, who provides the energy? The battery or the wall socket? If it is the battery, the power supply should continue to charge it, but it doesn't, because it keeps being cold (1); if it is the power supply - somehow bypassing the battery - it should again become hot as during the charge.
(1) Moreover, the battery would continuously charge and discharge around 99% - 100 % and this could damage it.