The core rules should also include variations on how to run low-magic and high-magic settings.
I would actually kind of like to see a bit of a throwback to the B/X/C/M/I days in one aspect:
Re-define "Epic Level" to be around 12th or above, and put all of those high-level class abilities and 6th+ level spells into a seperate Epic-Level Handbook. The PHB spends far too many pages on stuff that a large percentage of players never actually use. I think it kind of takes away some of the mystery of the game, and can also feed that "gotta plan out to level 20" mindset. But mostly, I'd rather see those pages used for more lower to middle-level content that is more likely to be useful to a larger number of players more of the time. The PHB could include more lower-level spells (such as from the Spell Compendium) without having to cut the "non-iconic" spells to fit everything into the book.
I don't really like the idea of combining the PHB and DMG into one book. It puts in a lot of extra pages that the players don't need, which increases the price of the book. Plus I'm even less likely to use magic items that are in the books that all of my players have sitting in front of them at the table. Not that they don't all have their own DMGs anyway, but at least I can ask them not to refer to them during play.
The usual supplemental splatbooks that will inevitably come out a year or two afterwards would be far more appealing to me if they were more than just a "Fighter Book" or "Wizard Book" full of generally unrelated concepts for Fighters or Magic-Users. Rather than splatbooks based around mechanical concepts, I'd rather see them based on campaign styles or settings with options that apply to all characters. GURPS supplements generally work like this. Once you buy "Fighter Book" you pretty much need to buy the rest or else all of the players with Fighters have far more choices than do the other characters, and the arms race begins anew. Plus I don't use about 90% of any of the "Complete" books in any one game. We've worn out this model already, between 2e, 3e, and 3.5e.
A new model of magic specialization would be welcome. 2e's "schools of magic" specialists robbed the Illusionist of pretty much all of its flavour and uniqueness from 1e, and 3e ripped away the rest of it. PHB2 and Unearthed Arcana helped bring a bit of that flavour back. Some of the schools of magic are flavourful enough, such as Necromancy or Illusion, but Transmutation and Evocation are really general and bland.
Reducing the dependency on magical healing would be a huge plus in my mind. They beefed up the Cleric in 3e to make them more appealing and a lot of players still don't want to play them. Not really sure how to best accomplish this.