USB NiMH charger keeps drawing same power forever?
That BTY charger has no charging controller.
  Why does the charger keep drawing the same power forever?


Because it contains nothing more (expensive) than a resistor. That is the cheapest way to produce these chargers.

At currents below C/10, you won't damage the battery too badly when overcharging. But this also means that a ~2Ah AA battery will be full tomorrow instead of today.