In my opinion (and other opinions will vary) it's kind of like the hot dog carts in New York. You can make 'em at home, but the experience just isn't the same.
The Italian Beef however...sure you can try to make it at home, but it really is impossible to reproduce the flavor of Italian Beef at a Chicago restaurant. The spices used, the pot used, the length of cooking time, all of those things are practically trade secrets.
Try a slow cooker. It takes a day or two to get the right texture. My wife can duplicate pretty near any seasoning we encounter in a restaurant. My daughter can improve on it.
You understand fully, why having Chicago dogs, and Italian beef from a Chicago restaurant, or hot dog cart, or drive in or hole in the wall place is different from making it at home...thanks...
What I find is that, while the spicy giardiniera peppers are tough to find, but findable, it's impossible to get the bread right.
Ultimately I think what I miss isn't so much the sandwich itself, which I can reasonably reproduce, but being able to get one within three blocks of anywhere I'm standing.