It's certainly true that when you cook with alcohol, some of it makes its way into the final product, even when you flambé or whatnot. Still, several classic dishes just won't be the same without the alcohol in them. Bread pudding without bourbon, poached pears without port, steamed mussels without a white wine and butter reduction, beer-battered fried fish without the beer... Sure, you can do any of these dishes without the booze, but they're just better with than without.
Also, it's worth noting that alcohol is a hell of a solvent, and many different flavorings that you add by the drop come with an alcohol base. Most notably, most vanilla extracts are alcohol-based. Also, bitters like Angostura, which are normally used by the drop in cocktails, are also used to flavor foods and soups.
On the flip side, I agree with Bitt that I dislike many things made with coffee, like tiramisu, where I find the coffee flavor overpowers everything else.