Some phones do too, it depends on their power management integrated circuit (PMIC) and driver. Though it's always better to physically disconnect the battery when not in use, as there is always a trickle current otherwise (most "spicy pillows" batteries are due to deep discharge, as far as I know). The best practice is to store batteries disconnected, at 60% capacity). In theory you could build a small circuit to sit in between the phone and battery to protect it, maybe I'll have a go at it.