I drive mine almost every day so long as it's not pouring. If I had a top, I'd probably drive it then too!
Since completing it in mid-May of this year, I've racked up 8500 miles. The supercharged 302 gets 23-24 MPG (IF I can keep my foot out of it!) which is definitely better than the rest of my "fleet"
If you're going to use a Cobra as a daily driver, you just have to get used to poeple looking at it, getting way to close to it, touching it, etc. I usually don't worry about parking it in a public place because it's the most watched car on the lot. I haven't found anybody sitting in it yet. Not sure what I'd do!