To be fair, most of the concepts aren't new in 5e. Most of it is refinements from 4th edition, with the concept of Limits added in.
And don't forget that the GM is always able to make judgments as they go. Like I said, I frequently call for a character to make a "luck" test by rolling pure Edge Rating. Or an Intuition test to see if their character can put 2-and-2 together. Usually, those types of situations are when the players are having trouble and I need to give them a push by saying that they realize x-y-z...
If you can think of other Attribute-Only applications that seem appropriate, similar to the ones that are already presented in the Rules, I'm definitely interested in hearing some other options. Off-hand, I can't think of any other good examples of a two attribute test that could represent a specific type of action.