What I am suggesting is close to the Badge Case that got added in the 6.3.2 update, as it would be a way to store badges, but that would not be the main reason for it. What I am suggesting is for more showing off your badges to others on the servers, and the only way to do that as of now is with item frames, which is not very secure as anyone can break them and steal your badges. Also they are quite bulky to even show 8 badges.
With the new badge Case is, you can only show others that you give a copy of your badge case to, and both are on at the same time. Now what I am suggestion is a way to show off your badges to anyone.
How would it work? Well, in my mind, it is connected to your badge case (maybe even use one in it's recipe to craft), you click on it to access the badges in the case and choose 4 badges of those you have earned and they get showed off in the case while not being able to be stolen