Here's a quick video to show a failed edge selection, then one that succeeds.
Here's a screen grab of a single edge selection. Note that selecting just this edge will fail a fillet. But, look what would have to change for a fillet to go "only on that edge!" Selecting the little curve in the adjoining fillet will allow the filleter the knowledge to create a little cap there.
Also, if you start looking at it from a single edges picking fillet process, you can see how you can get backed into a corner. At this corner, you would need to practice more advanced, lower level modeling techniques to finish.
