YES! This is what my analysis has always led to too - which is why I keep noodling with trying to use the 5e SRD to produce a 4e retroclone but never really pull the trigger on it.Thinking about it a little more and looking through some old notes, it would be almost trivial to recreate the AEDU system under the OGL. With short rests and long rests a standard 5E mechanic, simply have always available abilities (cantrips/at-wills), short rest abilities (encounter), and long rest abilities (dailies). 5E already works that way. It's just "hidden".
There's a lot of 4e mechanics in the 5e SRD, even the math is there just at a different scale. You have to put the grid back in to get the feel to work, but a lot of that is just translating feet back to grid measurements which folks often do with 5e anyway.
Looking at the PHB1 and the fighter, there are four at-wills. They're all [1]W + rider. The riders are: STR mod damage to second, adjacent target; damage on a miss; +2 to-hit; push the target 5ft.
Just rename those stunts (or something) and have them all always available when the fighter attacks. Maybe add in one or two other simple riders. +2 damage. Pull the target. Shift the target. These could literally be a list for the fighter to pick from with every attack. It solves the problem of the players who want simpler characters ("I just want to swing my sword") and the problem with players getting bored with their locked-in power selection.
I like this. I'm going to keep watching this thread and when I get some free time see if I can contribute anything I've got scratched out in my various notes.