I have a story for you. Once I went to Nordstroms in San Francisco (this was probably 4-5 years ago) and bought a beautiful rabbit fur/felt hat. When I asked them if they sold hat boxes to store them in, they had NO idea what I was talking about. Macy's was the same: those overgrown teenagers there didn't know what a hatbox was either.
Finally, I was in Ross one day, looking for other things and I stumbled upon some hat boxes. Unbelievable. I had to go to a place which probably never sold a decent hat to find a decent hat box.
If you buy a hat at Saks,they put your purchase in a hat box.
When I had the hat I wore to my daughter's wedding made (I used an atelier,so that's different),they packed it in a hat box,as they did with her wreath and veil.
But,the last hat I bought,got stuffed into a shopping bag. It wasn't a "good" hat and I bout it when I was on vacation,the store was NOT a department store,so I just figured that's why they used a shopping bag.