[m4rtink]

For any heat engine - including a stirling engine - you need a heat difference between the hot and cold side, ideally as big as possible. If you put the stirling engine at the bottom of the hot hole, the whole machine will be hot, there will be no difference in temperature and it will not run.

This also discounts stuff like the need for maintenance, that is hard to achieve at the bottom of a hot & likely very humid if not water filled borehole.

For that reason, most geothermal systems pump water down & then back up again (possibly using multiple wells) & have the heat engines at the surface, where they can be easily serviced & a good heat differential can be achieved, via air or water cooling.

This in the end, is generally an industrial operation though, not really something suitable for every single house. Still helps with maintenance, as you can provide energy for many houses & don't hat to maintain the geothermal power production equipment for each house separately.