Extract enough heat from Earth and Earth loses its magnetic field and then its atmosphere and oceans (from the effects of the solar wind) which sounds like a negative externality to me.
While it's true we would die first, I bet we'd transition to other power sources even earlier. If we ever get fusion working reliably, that will probably be more convenient than geothermal, and at that point the geothermal plants will start slowly going defunct with no replacements.
If you haven't done a calculation incorporating an estimate of the heat content of the Earth's interior, then you cannot know whether humanity will be dead by then.