If you pay $30 for an armor set, you can only use it for the class it was made for. That means if you by a Necro outfit, you can not use it on Barb or any other class.
As a comparison, in PoE (I’ve spent $1000s), ALL cosmetics can be used on any character class. You play $25 for body armor it can be used on any class, male/female, doesn’t matter it works on every character as you please. GGG artists created the art and animation that goes into each cosmetic to be compatible for all and any build.
Blizzard, it’s a grave strategy to squeeze as much money out of your player base. Until improvements are made to accommodate the players and display a sense of appreciation for their support, the cosmetic shop is a hard pass for me, and hopefully others will too.