First off, deep discharging Li-Ion batteries would kill them. But the manufacturers are aware of that and set limits on how low their batteries can be drained to. So what you see when the battery appears fully drained, is often about 40% of the battery's capacity. (Even that level is not safe if left too long, as self discharge will start killing off individual cells as they drop below a certain voltage, and they then can't be recharged.)
That said
calibration is a real issue for devices, even if not for the batteries themselves. The calibration of monitoring circuits for Li-Ion are very straight forward and work within the limits built into the charging circuits of the device. It should not need repeated charging at the top end. In fact Li-Ion batteries can also be damaged by over charging, the harmful plating effects can start at relatively low levels of overcharging.
It would a good idea to let your device discharge to zero once in a while, but be sure to fully charge it to 100% soon after. The majority of the time though keeping the charge level up over 50% will be better for your battery.
Luck;
Ken