Mearls has talked about keeping 5e as "evergreen", which pushes down thoughts of 6e some. Why spend resources (= money) several years before it can recoup those costs if the sales of the books stay high? And even in the gluts of 3.x and 4e, the core books sales stayed high.
But, just in the spirit of the question, here's some thoguhts off the top of my head what I'd like to see in an all-new edition:
* More tools or guidelines for DMs to tweak the classes based on their table and setting.
* Better balance between different resource recovery models (long rest, short rest, at-will) so that different DMing styles or narrative needs for a particular adventure don't hinder or highlight one model over another.
* More detailed multi-roll systems outside of combat. The concept of a Skill Challenge was good, but limiting it to just skills plus the horrid* mechanical implementation didn't help.
* More options for abstracting parts of combat. One example I see people doing in 5e is treating groups of much-lower-level NPCs as swarms. So being able to have swarms of goblins, or treat the crew of your ship in such a way that they interact with the battle but are still quick and few rolls.
* Somewhere halfway between there - can I do a non-lethal bar brawl in a fun, narrative, and quick way that doesn't involve round-by-round tactics? Same for the higher level party taking out a bunch of goblins. A few rolls, a quick montage, 5 minutes of wall time at most.
* Make Inspiration more then just a bolt-on that many DMs ignore. Integrate it into clases and such. (Such as old Vampire:the Masquerade had doing things that met your internal or external natures to recharge things.)
* Keep the concepts of Concentration and Upcasting.
* Have other long term attrition options for the DM to use besides Exhaustion and HD.
* Keep classes (mostly) not getting more powerful abilities until 3rd or 5th to prevent multiclass cherrypicking. However, make classes get at 1st so they don't suddenly change play style at 3rd. (For example, the Scout subclass that doesn't get needed skills until 3rd needs to get fixed.)
* More use for other ability scores for every class.
* Less reason to rush to increase your "prime" ability score to cap because mathematically it's often the strongest choice in front of customization. (Maybe modifiers change slower like every 3 steps, or change slower as the modifier increases, or other way to say "it's just fine to play a character with a +2 or +3 in your prime ability score, that won't stop you from being reasonable.)
* Grant more 1st level customization options ... and make beginners able to make a character quicker. I put these together because they can be contradictory so need to be considered together. I can create a 1st level character in 15 minutes and find it lacks oomph and uniqueness until later levels, but working with brand-new-RPGers I've taken four hours or more to explain options, how ability scores interact with classes and how races interact with ability scores, spellcasting and going through spells to pick, etc. An example of this type of rule would be to give an ability score modifier from race (choice of a few), and then an ability score modifier from class (choice of a few) - that can't go to the same one. Suddenly any race can play any class, while still feeling like that race.
*Increase focus on background, both fluff and mechanically. That a sorcerer criminal makes a reasonable thief, and an sage fighter makes a reasonable learned man. One way would be making training a larger part of the bonus that ability scores.
EDIT TO ADD
* More design space given to races to keep them relevant. For example, each race has enough features that we can have a bare-bones larged sized race without breaking things. In addition have potential for racial advancement besides a small list of racial feats.
EVEN MORE BONUS EDIT TO ADD:
* Workable pets. (Beastmaster, necromancer, etc.). Putting action economy first (among other things) has caused consistant problems. Assume that an extra attack or two will still be shorter than the spellcaster and get over it.
* Multiple formats, with reasonable costs once you own the format to get it in another format. Hardcover, softcover, PDF, digitally integrated. Yes, the cost for some of those changes of formatting is real an needs to be covered - moving to PDF isn't just checking layout, it's bookmarking, putting in indexes, covering watermarking & distribution costs. Just like *cover have distribution costs. Digitally integrated even more so, and probably separate for each application. But being able to by a book for $30+format cost, and then rebuy the book for just $format cost plus a small convience fee - very nice. And working with 3rd party like D&DBeyond, that $format can go majorly to them, and iof someoen is buying content for the first time through them the $content cost cost mostly to WotC.