One of the most important reasons to clean brass is to prevent scratching your dies. It does not need to be shiny. As dies get more expensive in general or if you are paying top dollar for something like Redding dies, cleaning brass is important.
Putting the brass in a confined space and agitating them together helps remove gritty particles that can scratch dies or gun chambers. The process can be done wet or dry.
I don't hand load 5.7x28mm, but it is commonly cleaned by soap and water or "Simple Green" and water. 5.7mm casings are coated and many contend they will stick in the chamber if the coatings are removed by tumbling.
When I was young and poor, I put my brass in a coffee can filled with used and dried coffee grounds and rolled it under my foot while watching TV. This gives it a flat dull finish, but it is clean and it functions.
I got good results from putting my brass in a mesh bag and running it through the clothes washer until Mrs45 put a stop to that. I've heard of some using the dishwasher this way, too.
Many cleaning solutions, especially those with high ammonia content, should not be used in cleaning brass. This includes adding many kitchen scrubbing cleansers to your media. I have admittedly used a lot of Brasso over the years, but have stopped doing this.
I've done the steel wool thing as well. I chucked steel rods in my drill press and tapered them with files until they would friction fit the correct size case mouth. This is a tedious process and as the brass heats up under the steel wool the neck expands. This results in the friction fit on the rod slipping. This method resulted in a lot of split case necks for me. At my age I also avoid rags and such near spinning drill presses. I cheated OSHA a few times doing this method.
Brass cleaning becomes a "Time value of money" equation. If you are OCD like me and enjoy a little more labor intensive process, alternative methods can be rewarding. If you measure your time by how much money you could be making instead of playing with weird ways to clean brass, you should just use a tumbler or ultra-sonic. Having said that - I have long since moved into the "just tumble it" camp.
BTW- Tumbling media should not be difficult to get out if it is fresh and dry. It should pour right out of 80% of your brass and the rest may need a little help. Lyman media re-activater may help with this. My favorite way to get media out of primer vent holes is a brass 45 caliber cleaning jag screwed into an RCBS prep tool handle. The little point on the end of the jag goes perfectly into the vent hole and the body of the jag being bigger than the primer pocket prevents the tool from being wedged in the pocket. Any 8-32 threaded jag will work.