I'm going to start off by defining what I consider to be a Vancian-style magic system. Vancian-style magic is more than simply having daily resources - it's how those resources are replenished. In 3.Xe, Bards had a limited number of uses of bard song per day, Barbarians had a limited number of times they could rage per day. For both of those, they are renewed after a rest, on a daily basis. One can even think of them as spell slots, where the only spell a Barbarian could "prepare" is rage. Bards had the ability to gain alternate songs to sing with bard song (via Feats? I can't recall off-hand... thinking of things like curse song) and could spontaneously cast the specific bard song tune... up to the limit of their uses per day. But are those Vancian-style magic? Effectively, they are simply casting a spell a number of times up to the limit of their available spell slots.
I don't (and most people I've talked to don't) think that those count as Vancian. In D&D terms, spell slots and spell levels seem to be what most use to characterize a system as Vancian.
For me, it's even more specific: Having the requirement of replenishing your magical abilities from an external source, often involving actively choosing what magic to have prepared. In 3.Xe, Wizards use a spellbook; Clerics pray to a deity. Those are both Vancian. Sorcerers, who simply rest and regain their ability to cast spells, are not even though they use spell slots and spell levels to track what they can cast. (Aside: 3.Xe using spell slots and spell levels for tracking spontaneous casting was a lazy design that just helped reinforce the Wizard's status as the best class.)
So then, why isn't Vancian-style "magic" magic? Well, in a sense it is some sort of magic, but the character who wields it is not.
There's a trope called the Magic Feather which is about a character believing that they need a special/magical item in order to do their special thing. It's later revealed that the magic was within the character all along, and that the trinket was just a mundane item. Contrast that with the 3.Xe Wizard and the spellbook, where the magic is in the spellbook and the character needs it in order to continue to be magical. Once the Wizard is out of spells, the Wizard is out of spells. Without a spellbook to gain new ones, said Wizard is limited to things like scrolls, wands, and similar items that have magic stored within. Let me reiterate that: the Wizard is still only using magic bound within items, not from some innate connection to a source of magic (be it an internal source or external source) - that Wizard has no ability to simply reach out and manipulate the magic that already flows through the world. Additionally, lacking an innate connection to a source of magic, any magic the character does perform amounts to repeating something learned through rote memorization. (Indeed, understanding of magic and spells was moved to the Spellcraft and Knowledge: Arcana skills, neither of which was actually required to cast spells.) It gets even worse when considering that some spells required mundane material components that were consumed during the casting of the spell. (A focus for certain spells I can see as a requirement, but needing guano for Fireball? Really?)
How magical is a character who has had the item(s) that allow that character to perform magic taken away? Not at all. And so I am perpetually dumbfounded by those who think Vancian-style "magic" to be magic(al).
This was handled much better in 4e, with always available At-Will spells, and Encounter and even Daily spells replenishing after the appropriate rests without the need for a spellbook. Changing which spells the Wizard had prepared required a spellbook after an extended rest, but if the Wizard was simply going to keep the same spells prepared from the previous day then the spellbook was not needed. The 4e Wizard had an innate connection to a source of magic, and was not dependent on a spellbook. It helped, but was not the source of the Wizard's magic. (And likewise, even though in 4e every class can choose Daily powers, since they recharge naturally after an extended rest I don't think of any class in 4e using Vancian-style "magic"...)
I realize that by now, Vancian-style "magic" is a D&D tradition. By all means, let it be an option for D&D Next. But can we have Wizards (and other spellcasters) that are themselves magical and aren't wholly reliant on a crutch? Can we have a better magic system be the foundation going forward? Please?