The short answer is that you often do get sinkholes or [subsidence](https://www.usgs.gov/special-topics/water-science-school/science/land-subsidence). That is, the overall level of the ground will drop. This can be a real problem for some cities and is one of the downsides of pumping excess water out of aquifers.
This is less of a problem for oil because it tends to be trapped much deeper down and supported by non-porous rock above and below. But, it’s a serious problem for pumping water.
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