They're classic for country sporting coats, where you’re engaged in an physical activity like swinging a shotgun or casting a fly, and need to have something extra to keep stuff from falling out of your pockets. Ditto for riding coats. Here’s a shooting jacket.
I used to have a Norfolk with flapped patch pockets. Might even have been pleated bellows pockets. I can’t remember.
Let’s not forget that the pockets of country sporting jackets were (and sometimes still are) used for stuff: shotgun shells, sandwiches, pipe and tobacco, etc. The lack of flaps on a city jacket is as much about saying what it’s not as what it is.