Really, the more I think about it, the only thing from 4e that needs to be redone are classes and magic items.
I like your post and agree that they shouldn't throw the baby out with the bathwater, but what they should do is evolve, mature, develop "the baby." This means taking the power structure--which is an awesome idea--and notching it up a bit by differentiating power sources. Right now they feel too homogenous, with what I was calling a "too transparent sub-structure." In a way there are only four classes: Strikers, Controllers, Leaders, and Defenders; that makes sense from a combat/tactical perspective, but what is missing is distinct and unique flavor and qualities for the different power sources. An arcane striker and a martial striker should be very different, and not just in terms of fluff; I'd like one to be able to do things that the other can't.
In that sense, I'd like to see arcane powers be more like spells from previous editions; looking over the wizard power list in 4E just doesn't have the same evocative feel that it did in previous editions with the never-ending spell lists.
I also think that the Feat system is clunky to say the least. There are just too many feats, and too many useless ones (I've often wondered if there are some feats that have literally
never been chosen by any D&D player anywhere). I'd like to see Feats scrapped and replaced by something akin to Talents or Traits, or even a Virtues and Flaws or Advantages/Disadvantages system that provides a wider variety of capacities and flavorings to add to a character (although the problem with Virtues and Flaws is that it is another opportunity to min/max).
Finally, while I think 4E is generally a blast the main flaw remains the "grind" or, specifically, the point at which a combat is essentially decided but still goes on for another few rounds. I can't tell you how many times I've ad hoc reduced monster HP just to end a grinding combat. To put it another way, 4E combat is great for the first half of a given encounter, not-so-great for the second half. Maybe the implementation of a deadlier mechanic, like "When first bloodied, make a saving throw or fall to 0 HP and unconscious" (or maybe an adjusted CON check instead).
But yeah, the core of 4E is great and (IMO) an improvement and evolution from 3.5. That should be the basis of 5E, not a return to 3.5, nor something completely different. Most of the issues that lapsed players have with 4E isn't, afaict, about the core but the general vibe and the details and/or secondary systems.