"Core 3" Worked for me in 3E and 3.5 because I always considered everything in the PHB, DMG, and MM to be very well balanced, applicable to all campaigns, and not so "out there" it couldn't find a place in 90% of D&D campaigns out there. When any of our DMs said, "core books plus this other stuff", we knew what it meant, and worked off of the same base.
My largest concern is that the material in the later expansions will not be nearly as well tested as the original set, and problem rules will slip in through the cracks (like, oh say, the Energy Missile as originally written in the Expanded Psi Handbook, or the Frenzied Berserker in Complete Warrior.

) Even the much-vaunted Druidic shapechange from 3.5 that was touted as "game-breaking" I've never seen a problem with, only heard second-hand. Having "core" be very open-ended means a larger pool to stuff to pass/fail on a case by case, and DMs having to go case-by-case what they will and won't allow in a given game.
Me, I dislike the idea of Tieflings being a core race from the start, just on general story grounds; it presumes to me a much more default planar-open cosmology than I'm used to. Maybe I'll change my mind when it gets here, but on first blush I am very hesitant about it, as one example.
So when I tell a group, "I'm starting a new campaign, core books only," I'll instead have to say,
"I'm starting a new campaign, all PHB 1 races except Tieflings and Eladrin, all classes from the PHB 1 except Warlock, Include the bard from PHB 2, and exclude the new ability from the bard's such-and-such talent tree," or something similar. or worse -- go back to that ugly tradition from 2nd edition, and make pages of house rules of what's included and excluded from each book in the "core" series, as well as any expansions.
OR.... I've just treat each game as its own totally separate entity, and run totally different types of campaigns for 4E than I would for 3E and lower.