I don't find this to be a very compelling argument. Characters sometimes do things that might require split-second thinking which can require an ability check to resolve. The key part there in my view is that the players are the ones deciding what they are doing. As a save, this would look a lot more like Defy Danger from Dungeon World which I would prefer. "The flames explode outward from the tiny red sphere - what do you do?!" "I hit the deck to avoid the worst of the flames!" "Okay, let's see a Dex save..." versus "The flames explode outward from the tiny red sphere - make a Dex save." Here the DM (and the mechanic) just assumes what the character is doing.
In many cases, the mechanic used to resolve the uncertainty would be the same, but at least the method I propose would be more in line with the basic conversation of the game wherein the DM describes what's happening, the player describes what he or she wants to do, and the DM narrates the results. Saving throws as written assume what the player wants to do and that's not my preference.
If there is to be no input from the player outside of ability score choice at character build or advancement, then it may as well just be a defense as in D&D 4e in my view.