We'll (and humanity itself) be long dead by then

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.

Assuming just the inner core, using the lower bound for its temperature, specific heat capacity of iron, 20 TW being extracted, ignoring the extra power inputs in the form of radioisotope decay, crystallisation, tidal heating, I get 800 million years, which is close to when photosynthesis stops because of geological processes locking all the carbon away (trees stop working at about 600 million years, not sure about plants in general).

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.

Extracting enough energy to do that, would probably meltdown the earth crust.