A little knowledge is a dangerous thing. Once you know a little about X you might think you know everything you need to know.
Like if someone shows you some cute fairies you might think you know about fairies and be screwed when you meet some non-cute ones.
Or if the wrong person overhears you saying "We can't go to that club; my cousin says that's where the white power sex vampire live" and decides that you know enough about the white court to be a threat.
If you see <supernatural creature A> and assume it has something to do with <supernatural creature B>. Wyld fae, summer court, and winter court are very different creatures and if someone thinks "Oh, that a fae" and treats it wrong...
Basically, there are all sorts of ways a few misunderstood facts can get mundanes in trouble and most wizards are drilled with that knowledge. Think back to the early books where Murphy is kept in the dark "for her own protection". Or Harry's sometimes student who died in Fool Moon because he wouldn't share information with her. Slowly he changed a bit and told Murphy more, but he still has a lot of "Wizard knows best" in him - and Harry isn't one of the more arrogant wizards out there.
Then there's the Merlin / Julia problem from the Merlin cyclic of Amber books. Merlin (a son of Amber and Chaos) is a very special dude with lots of magical powers. Julia is a nice girl he gets involved with. One night Merlin shows Julia a bit of magic and it poisons their relationship - she wants the power but he can't wave a magic wand and give her power. She wants knowledge that would be dangerous to know. She thinks that he's keeping things from her and he is - most of the magical side of his life. After the predicable breakup, Julia goes looking for magic - and in the second chapter of Shadow Knight Merlin finds what's left of her body after a hellhound used it for a chew toy.
Just imagine:
Wizard: "Hi, I'm your Uncle Bob and I'm wizard. Watch this!" <does cool magic>
Family Member: "That's great! Can you teach me to do that?"
Wizard: "Um, you don't really have enough magical talent for me to teach you, sorry."
Family Member: "Then can you help my friend? He broke his leg - can you fix it for him so he can go jugging today?"
Wizard: "Um, magical healing doesn't work that way, so no."
Family Member: "Then can you make me super strong so I can get on the wrestling team?"
Wizard: "Um, changing you that way would be wrong."
Family Member: "Then can you make Mary Beth Tailor fall in love with me?"
Wizard: "Um, doing something like is wrong. There's free will and..."
Family Member: "So what the $&^# good are you?"
Or:
Family Member: "Vampires exist? Cool! Let's get Buffy on their ass!"
Wizard: "Well the protocols dictate that when dealing with the White Court..."
Family Member: "What, you mean you know about vampires and you don't do anything? You just let them wander around feeding? How can you be so uncaring?!"
In short, Dresden magic doesn't work like fairytale magic, but will your family and friends believe that? Can they understand how the White Council works and why you can't bend the law of magic just this once? Will they misuse any information they give in a way that comes back to haunt you (or endangers them)?
I think those reasons, rather than White Council policy, are the main reasons that most Wizards don't live as openly as Harry does.
Richard