Should it really? Having owned a coffeeshop, if someone brought a cup of coffee into our store, they were asked to toss it or leave. Where's the revenue in having people imbibe someone else's product in your establishment?
It wouldn't work for coffee. In the case of New Orleans, the revenue comes from 4-5X as many people being there for the experience day after day than would be there without it. The people running the establishments know, and they get it. It's a big part of the appeal in the city. It's only 1/2 a beer or so.
Small example, but my sister lives in Aiken, SC. All the restaurant/bar owners along a particular side/alley (brick) agreed to do the same. They all have tables outside, they split the cost of live music and all agreed that anybody at any of the tables can drink from any of the locations. Business increased dramatically for all of them. If you and I are there getting dinner, and you want wine, but I want beer from the place across the way, now that works. I've seen the exact same thing in a huge square in Tours, France.
That latter example is more an example of what I think should become common. Most cities won't do what New Orleans does.