Seeing as this is all theory any way, I will disagree.
With a 20'x20'x20' (that is 300 cu yds of dirt !), then filled with water, the worse thing you would do is raise/lower the temp of the surrounding earth 5 or 10 degree.
The "thermal transfer medium" (the water) must be contained so it does not seep into the ground and it needs to be insulated from the ambient (ground level) temp, so the water should only be about 10' deep. That is 4,000 cu ft of water !
This is a complex problem and would definitely take some engineering.
The reason geothermal systems use well is that they are easy to dig. The reason they use multiple wells is to get more contact (surface) area.
The biggest problem is that you're really limiting the surface area is you're digging a single big hole and 'filling' it with water tubing. Most of the interior tubing isn't going to do a damn thing, and since you've got basically a cube, you're really limiting yourself. Given, you'll have a lot of water, so you've got a lot of thermal mass, but you're not giving yourself a lot of place to put that thermal energy.
Like you said, wells are best because you have a single tube that is completely free to transfer heat in any direction all the way down. Typically geothermal systems will require between 8 - 15 ft between wells to avoid heat soaking the ground. Of course, they are not 'easy' to dig since most end up over 200' ft deep, unless you've got the real estate to go horizontal.
Remember that these systems work off relatively small changes in temperature, so if you do increase the ground temp by 5 or 10 degrees, it makes a big difference in terms of cooling capacity.
Disclaimer: the above is coming from the perspective of someone whose been involved with some larger geothermal systems for commercial applications, where a small lose in cooling capacity is a BIG deal. For a garage, obviously temperature is not nearly as critical.