Once the well is dug, cased, and the pump is installed there are very little operating costs especially with solar-powered electric pumps.
The math for a comparison between a well and this gizmo would be interesting.
If you're not going to be in a particular area for very long, digging a well might not be an option. An AWG can collect water while you're moving -- all you need is access to air.
If you find yourself in an area where the water table is contaminated, using an AWG may end up being the safer option.
Imagine you're living in space (or a similarly resource-constrained environment): you've got multiple people losing something like 0.5+ L/day (citation needed) to the air through perspiration -- that's valuable water. Moreover, to keep people comfortable, you should make sure your relative humidity stays below 60% (citation needed), so you're going to be pulling it out of the air anyhow. NASA undoubtedly has these systems in place in space, but that doesn't mean we should develop a open source version of the equipment that everyone can collaborate on and improve.
TL;DR Sometimes you're willing to trade energy for water. Also, open source.
Most of the startup cost is in digging the heat exchange loop.
I'm not sure how to determine the practicality of well excavation, but my intuition tells me it largely depends on geographically influenced factors. I'll look into that.