I don't know if I should be messing with this, but here goes!
1. Don't just call it "D&D".
I've always considered 4e to be the purest, most honest interpretation of D&D, delivering on many of the failed promises implied from previous editions. In fact, I think it is more deserving of both brand and title than any others. But I believe it is more important that it stands out as a variant of the game rather than trying to own it.
4th Edition stands out because it is so radically different from everything else in the game's history. It is a derivative of the original game, so it deserves to have the name and brand attached to it. But in many ways, it clings closer to the core values and ideas of the game experience many fans have dreamed of since they first started playing. Player classes that were equally balanced and useful in every pillar. DM tools and guidelines that made monster and encounter building easy. A world cosmology that provided a place and reason for everything in the game to exist.
Despite all this, it is not what I consider "original D&D". This is new and different. It is another way to play the same game. It's an alternative, which makes it a choice. But surely there is room for more choices, right? So that's where I would start.
2. Essentials or Core: Pick a lane!
For those of you not in the know, Essentials was a last-ditch attempt to win over non-4e fans while simultaneously updating the 4e rules with better, more consistent rules and changes. This is where a lot of the inner 4e-fan base gets divided (as if the edition needed to be more divisive!) because, while the monster formats and rule updates were welcomed, the Essentials classes went against a lot of the core ideas and philosophies that a lot of 4e fans actually liked.
Personally, I liked both approaches, but I would prefer a more consistent approach. Either stick with the core AEDU approach, or expand the more "classic D&D" feel with the Essentials approach. Or redesign for something in between. Just make it consistent and don't tell me it's all compatible! My OCD says so!
3. Cut down the bloat.
I can't overstate this enough. There comes a point when there are just too many options, too many supplements, too many hit points, too many bonuses stacked, too many conditions, and too many decisions. Give me a core game that works effortlessly with as few books as possible. Create supplements that are entirely optional but will expand the whole game, not just parts of it (i.e. a book for Heroic characters options instead of one for Divine, one for Martial, etc.)
And for goodness’ sake, reign in the number (and range!) of modifiers in play. Make hit points reasonable so that every combat doesn't slog for over an hour. Less math and more play, please.
4. Digital (VTT) support/Open License support.
I think this goes without saying (and I'm certain it was implied in the OP), but it's something we take for granted nowadays. 4e was the one edition that was (and continues to be) excluded from receiving a decent amount of support outside the company that owns it. Enough said.
5. Endanger those Sacred Cows.
Do what works best for the game in order for it to work better. Instead of trying to appease the gatekeepers and grognards with a product that they won't be interested in any way, do not be chained to antiquated and outdated ideas of game design and philosophies. Being tethered to the original concepts and ideas of others subverts innovation.
Healing surges, for example, was a radical idea that worked for 4e, and kinda snuck in a little with 5e (using hit dice to heal). But it was underutilized, IMO. It could've been used to charge (or recharge) certain powers or abilities. Of course, the name would need to be changed (Heroic Surges?), but there was more potential that could be explored.
Maybe it's just me, but that's where I would start.
