I used to work with a guy who did this very thing. Dug a 4' hole and
put sand in the bottom, then installed the pool.

People don't tend to do this because the cost of digging the hole (and
locating/relocating all power, gas, water, and sewer lines) is high.

Check with whoever your planning nazis are, here you need a 6' fence
around pools. You may need a permit.

Never really thought about doing just a hole with membrane. Wonder
what the downside is if any.