The thing about the wig is it's alien.
You put on a hat or a scarf and it's an accessory -- decoration. It's part of you, your personality, your style.
You put on a wig and it's camouflage. And not great camouflage at that. You're worried it will move. Or that it won't move. Or that you will put your glasses on the wrong way, exposing its edges. Or that it just looks false.
Hats and scarves don't look false. And if they move a bit, it's no big deal.
Granted, with no hair peeking out from under my hat, I look like one of the seven dwarves, but it's a Look.
Here's my new hat.