[Chalky (OP)]

Geothermal seems a great idea.  But if we had pipes all over the Earth, and went about tapping it for energy, would we not just eventually use up another nonrenewable?

I've posed this question in the past, and I'm usually told it's a negligible amount, and there would be nothing to worry about.

If the latter is true, why haven't we just all switched over to geothermal?

[Petrochemicals]

I think not, unless we where talking starwars type super villanry, the earth radiates energy outward from the core anyway, all we are really doing is bridging the last few kilometers distance down from the surface and replacing that with water. The surface will not recieve the heat, but it will therefore retain more of the energy it recieves, mainly from the sun, which is the primary source for the surface as seen in such things as Sahara versus antarctica. All we are really doing is extracting energy from the surface before it reemits the energy outwart into deep space. This is all done with water and steam.

The laws of thermodynamics however show the problem that the atmosphere will now have more energy in it, leading to who knows what problem with global weirding!

[chiralSPO]

Geothermal energy is effectively inexhaustible over the next few billion years. There is a vast reservoir of energy left over from when the earth fell together, as well as an radioactive decay. That energy is being radiated anyway, all we're doing is harnessing it (like a hydro plant on a waterfall--the water is falling anyway, we're just extracting some of the usable energy and putting it to work). We are unlikely to be able to change how quickly the energy gets out by any significant amount.

But, I can tell from the question that answers like "very big" and "long time" are not satisfactory, so lets try to put some numbers on it:

According to wikipedia (https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget), and the primary source cited in the article (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012RG000400), thermal energy crosses out through the crust at a rate of about 45 TW.

About half of this energy comes from radioactive decay (and at this point most of this energy comes from nuclei with half lives in the billions of years, so that is energy we can depend on well after the sun cooks us all.)

The other half comes from primordial heat, from when the earth fell together. This is a diminishing resource, but it appears that at the current rate of cooling, even this has a few billion years before it would be a concern.
(https://geosci.uchicago.edu/~archer/deep_earth_readings/jaupart.2007.mantle_heat.pdf)
(https://www.sciencemag.org/news/2011/07/earth-still-retains-much-its-original-heat)

Globally, we currently use energy at a rate of about 20 TW.
(https://www.forbes.com/sites/quora/2016/09/22/we-could-power-the-entire-world-by-harnessing-solar-energy-from-1-of-the-sahara/#e4d1f20d4406)

So even, if we got all of our power from geothermal sources, and somehow did it in a way that the additional extracted energy were on top of what already comes out (which is a huge overestimate), we would only bring about a frozen earth apocalypse 50% faster than it would otherwise be.

As to why we don't use geothermal:
Firstly, we do (ever been to Iceland? They have the cheapest electricity in the world because it is almost entirely derived from geothermal energy)

But there are several issues with geothermal:
• It's only easily accessible in some parts of the world, and typically in geologically active areas, which makes building expensive power stations somewhat problematic (who wants to build on a volcano, or somewhere that has . multiple earthquakes per day?)
• It is possible that boring the wells needed for extracting the energy could trigger additional geological activity (you wanna tap a supervolcano and risk causing it to blow?)
• Without suitable energy storage and release tech, geothermal power is best suited to applications that need constant power output (like heavy industry), and not well-suited to the daily up and down of residential power demands.