I think that you could do the Dresden-verse in d20. Preferably with a significant variant, in the way M&M did supers (which, until I looked at that system, I thought d20 couldn't handle).
First, you'd have to create your own magic system. Off the top of my head, I'd do evocation and thaumaturgy with totally different systems. Evocation would be relatively simple. A few relevant feats, and a skill for each element. Make a skill check and spend vitality (I'd use the wound/vitality system from Star Wars and Spycraft) to cast a spell. Spells themselves are very roughly defined, in much the same way regular skill checks are. Alchemy would be its own skill, with a whole subsystem for determining the final potency (and effect) of the potion based on the ingredients added and the skill check. Thaumaturgy, I'd have to research. Despite it being Harry's stronger ability, it's described in much less detail in the books. But, again, I'd probably assign it a suite of skills (e.g., Summoning, Wards, Scrying), and define how each skill works separately. Thaumaturgy probably wouldn't cost vitality, but, rather, would have some other cost, and would have a large time component.
Second, you'd have to account for different creatures. This is probably easiest done with level-adjusted races. So, a fey costs you, say, five levels. Then, you can become a warrior, or a mage, or a priest, etc. Maybe actually make racial classes, so that you can represent fey of different inherent strengths, and so that you do things like gain werewolf after a few levels as a human.
For the basic class/skill structure, I'd probably fall back on d20 Modern. As a devoted Spycraft fanatic, that pains me. But, the Dresden-verse involves far too many people who are very low-powered and common. d20 Modern does that scenario well.
I'd want to define a few other subsystems, like Faith. Things that have a decided effect in the Dresden-verse, but aren't, strictly speaking, magic.
The biggest challenge would be maintaining the feel of the Dresden-verse. d20 is, by its nature, a very tactical game. Even when used for intensely socio-political games, it's very tactical. The Dresden-verse, OTOH, is pretty fast-paced and seat-of-your-pants. Now, there's no reason you can't play in the same universe with very tactical characters (e.g., playing out the Wizard/Vampire War). But, it will be a pretty radically different feel.