For your example: A 1/2 acre home is 2023 m2, 1kg of rock is ~2000j/degrees Celsius, 1 cubic meter of rock is ~2500 kg, down 1k = ~2000 j * 2500 * 2023 * 1000 / 60 / 60 / 1000 ~= 2,800,000 kWh per degC. If you’re talking 1kw of heat on average from that rock you only drop 1 degree after 300 years.
Of course 1km is a fairly deep, but if you’re using a heat pump chances are you’re averaging much less than 1kw over the entire year.
Much higher ground temperatures are of course useful to create electricity, but such systems are best centralized not used for single family homes. Also, as a centralized system it’s volume is arbitrary. In the north that 6-25C can still make heat pumps vastly more efficient, but you’re extracting energy and cooling that down over time. Which is why it is relevant to the discussion.
The energy flow from the Earth's core is small in a percentage sense, but keep in mind that humanity's energy use is actually tiny when measured on planetary or cosmic scales. Here's the total solar surface area we'd need, for scale:
https://www.axionpower.com/knowledge/power-world-with-solar/
Cover much of New Mexico with solar PV and you could power all of global industrial civilization (ignoring storage).
Though usually you’re pumping more heat out of the ground than in. There must be a perfect place for these systems where it’s well balanced.
Also, I think a lot of wells add concrete casing (or metal, as indicated in the article) around portions of the well, which would prevent extraction around those zones of the well.
caveat: thinking like a physicist, not an engineer :-)