That’s roughly how open pit mining works. In some mines, you start with a pit, but later make a mine shaft if you need to go even deeper.
A pit is relatively cheap to start with, but it becomes more expensive as you go deeper. Eventually, a traditional mine shaft becomes cheaper than continuing with a pit.
If you have a ridiculously deep mine shaft, you begin to run into various problems like walls collapsing and the temperature increasing. There can also be lots of water you need to pump out constantly.
Eventually, the shaft becomes so deep and the problem so large, that continuing becomes a nightmare. That’s why even the deepest mines aren’t really that deep considering how thick the tectonic plates are.