Ms. McArdle is right; if you look too closely at the relationship between magic and the real world in Rowlings’ world, it doesn’t hold together very well.
Any time a creator introduces a fantastic element to their story, it vastly complicates things. On the one hand, magic (or its equivalent; as Arthur C. Clarke noted in his famous Law, “Any sufficiently advanced technology is indistinguishable from magic”) is a great way to jazz up a story. On the other hand, you run smack into the “deus ex machina” hazard.
It happens a lot in comics. During the 1970’s, Superman had grown so powerful that it was almost impossible to generate any real dramatic tension — he literally could do almost anything. DC had to “de-power” him a bit. Even then, they had to bring enough kryptonite to earth to rebuild his entire home planet several times.
A few authors have managed to pull it off quite well.
David Eddings, in his Belgariad/Mallorean series, described magic as “The Will And The Word.” The sorcerers in his world can do almost anything, within some limitations. All they have to do is muster their will, focus their attention, and release it with a word.
The drawbacks are that using magic can be physically exhausting — so for most tasks, it’s easier to do it the “mundane” way. Also, the laws of physics still apply; one character uses sorcery to lift a giant rock, and sinks himself into the ground up to his armpits.
Another limitation is that one cannot unmake anything. Attempting to do so tends to disintegrate the sorcerer.
Finally, it takes a very specific confluence of events to unleash a sorcerer’s ability. They have to be worked up enough to have sufficient determination, a very specific goal in mind, and it has to NOT involve obliterating something. Many would-be sorcerers found their first of sorcery to be their last.
Another creator who found great ways to deal with beings of great power is Joss Whedon, the creative deity behind Buffy The Vampire Slayer, Angel, and Firefly. In the Buffyverse, vampires and demons are tremendously powerful, and very few humans can stand up to them. He balanced this out by giving them weaknesses and vulnerabilities, and also had one of his characters (Spike) explain just why he had no interest in conquering or destroying the world:
“We like to talk big, vampires do. ‘I’m going to destroy the world.’ It’s just tough guy talk. Strut round with your friends over a pint of blood… the truth is I like this world. You’ve got dog racing. Manchester United. And you’ve got people. Billions of people walking around like Happy Meals with legs. It’s all right here.”
And my most recent discovery, Jim Butcher, the author behind the Dresden Files. His protagonist, Harry Dresden, is a wizard — and lists himself as such in the Chicago Yellow Pages. He’s an amazingly powerful wizard, and his world features demons, werewolves, faeries, and vampires — lots and lots of vampires — all living unnoticed among us.
There are drawbacks to Dresden’s power, though. For one, he does not get along with technology. Gadgets of all kinds tend to screw up in his presence. He drives an ever-increasingly-battered Volkswagen Beetle (it’s so simply built, it tends to resist his influence) and his apartment doesn’t even have electricity.
Further, we humans can — if sufficiently riled — wreak havoc on the mystic forces if we set our mind to it. The above-mentioned technological incompatibilities work both ways, sometimes, and magical defenses against high-powered weaponry is spotty at best. So the dark forces find it to their benefit to keep a relatively low profile, allowing people’s natural instinct to deny and ignore inconvenient facts to keep things quiet.
Rowlings doesn’t do that. Her magic doesn’t come at any great price to its users, and for most hings it’s far easier to use magic than to do it “muggle” fashion. There is also no real reason why the muggle world isn’t far more aware of the magical world, other than plot convenience.
However, as Ms. McArdle notes, that doesn’t really get in the way of a hell of a great story. And Ms. Rowling, if nothing else, is a hell of a great storyteller.