I wouldn't mind seeing a certain redistribution of materials, but I don't think a single book is a good idea.
I'm firmly of the mind that the players don't need to see the monsters, so I'd like to see them in a separate book. I could buy into including animals in the PHB, though. That'd solve the two most common issues: mounts and familiars. I could also see some downside to splitting up monster stat-blocks, though.
It'd be great to have the condition summary stuff in the PHB, so that I could just tell the players, "You're fatigued," and have them understand or look it up on their own -- I regularly have to stop the game to supply a summary of a condition to a player. Since WotC have decided to put PrCs in player books (pretty much every book, actually), they may as well put the handful from the DMG into the PHB, too. The variant character creation (esp. point buy) should be in the PHB, too.
Magic items should stay in the DMG, since they're treasure an "examples". I'd rather see players encouraged to come up with their own stuff. Of course, if you're running a "magic items on the store shelves" game, the opposite is true.
I'd also like to see a lot of the cool things from the 1E DMG thrown in: better quick personalities, herb properties, gem properties, dungeon dressing, colors and other descriptive words, etc. The DMG is, also, the right place to talk about cosmology, divinity, and epic levels. Of course, a chapter, each, on adventure design and worldbuilding should be the meat of the book -- from the sounds of it, the DMG II might be a better DMG than the DMG. Even after a couple of decades, there are quite a few little tricks that I know, but tend to forget.
As far as cutting stuff, I could see quite a few spells moved to expansion books (Complete X). It also wouldn't bother me to see Druids, Bards, Paladins, Monks, and maybe Barbarians and Sorcerers moved to a "Complete" book. Many DMs get all the Complete books, anyway, so no harm shuffling some things that way. The plus to WotC is that more players will probably pick up these "Complete" books. Even some feats could be shuffled that way. Do I think these things need to be moved somewhere else? No (okay, maybe paladin), but I don't see it as a violation of any principles, either.
Ultimately, I'd like the PHB to be all the main rules. The stuff a body needs to play the game -- to follow the action.
The DMG should be, primarily a resource for "downtime" when you're creating or reviewing an adventure. You know, stuff that might guide the DM in setting up the game, but probably won't be needed at the table. Not just advice, but something reusable.
The Monster Manual is a collection of critters and rules that specifically apply to using, creating, and advancing them. The DM may need this at the table and during planning, but it's still a dedicated book.
I like the UA book of variants, too. Maybe not a core book, but definitely something that I hope sees print for all future editions of the game.