'Snap to point' in Illustrator is poor. You cannot currently snap objects together reliably. Results are inconsistent.
For example:
1) snapping a point to an edge does not work well, if at all. I have 'snap to point' on and smart guides enabled.
2) when using constrain with the Shift key, whether they be points or edges. Even with Snap to Point turned on, or using Smart Guides. Just something simple as drag-copying another box adjacent to itself does not snap together the edges.

In my videos, the first video applies to point 1) and the second video at 10s, you can see that when using 'constrain' there is no information about where the edges are, and snapping of the edges clearly does not work. Not even dragging a corner, which is a point, to the other objects' edge, no snapping or any edge indication.

Adobe please do not consider this. Please just fix it and make this work, please!