First time I heard about "Swedish egg coffee" from American colleagues I was really puzzled, had to do some research about it because I never heard or seen it. It seems to come from some Swedish immigrants to the USA that used eggs instead of fish skins to remove impurities from coffee.
I was skeptical but...it's actually great.
OfIs a clear broth actually something that matters besides a gate keeping technique in French cuisine?
Traditional French (beef) buillon is made this way, it's presentation and taste is specifically light as it's the starter course in a multi-course meal so it's there to just whet the appetite not serve as a stand-alone meal. The way that it' finished is using the egg technique to ensure it's clarified after being passed through a cloth and chinois.
It's the same way in Japanese cooking, in order to get a proper dashi you have to ensure you don't let things get to a boil because the katsubushi or my personal favorite niboshi can break up and then ruin it entirely at those temps and it will become bitter and unusable to make soups, sauces and braises with.
So, yes, it has a purpose beyond just looks.
Iirc you can also use it to prepare coffee when camping. The egg binds to ground coffee in a saucepan so it’s better separated from the coffee you pour into your mug