I used those boxes when I moved, they worked great for me!
If I didn't have a flat file I'd have no problem using them more permanently. I still use the smaller ones I have for stickers and random little art stuff I have.
If recommend still putting each of your prints in their own sleeve before storing them in the box.
Like a mylar sleeve? Most of the posters are about B2 size, with a few others up to 33x22. I'm wondering if a thin backing paper between each poster would be more economical