The charger does have 50 Watts of output power. But it takes more input power into the charger to generate that 50W of output. Power is required to operate the control circuitry, the light energy for the display has to come from somewhere, etc.

I have the DC version of the 606 and it generates heat too. Probably not as much as the AC job, as the internal power supply (and external ones) has inefficiency as well, as you suspected.

Regarding the lipo battery, yes they are quite efficient in their charge, very little wasted heat is generated in the battery itself. But unlike ni-mh or ni-cad, as they degrade & increase internal resistance over time, instead of requiring more voltage and thus power to charge at a given current, the lipo will switch from the fast CC mode to the slow CV mode sooner in the charge cycle. Peak power requirement is not impacted, but rather time is increased. This is due to the inherent need to carefully limit the maximum charge voltage of lipos.