Upon starting a new character, I decided to purchase Cadwell's Maul, Axe and Shield. This did cost 12k. It looked really great on a redguard in Nordic Bather's Towel

As I progress, I equip new gear. When I log out, and later in again, the purchased outfit styles are no longer present, and must be purchased again if I still want to have them "equipped".
I can't find any spesific information online adressing this situation. Is this really the way it works?
Do I really have to purchase the same outfit styles on the same character multiple times, as long as I change my actual gear?
Arinwyn ~ Cute Wood Elf Archer
Wardena ~ Frost Wardeness [Died alongside Arctic Blast]
Dry Spell ᕙ༼ຈل͜ຈ༽ᕗ
Dark Heart of Skyrim 🍺
Bomblebee ~ cya'll out there
Bouncing Betty ~ Front Toward Enemy
Spearpoint ~ Jab Them With The Pointy End
Six Feet Above ~ Reapertime!
Bisolar Disorder - Bright & Moody
Django Unleashed ~ Mr. Nordic Bather's Towel
Master Angler ~ Struggles With Ichthyophobia
Ichthyophobia ~ Secretely Dreams of Becoming a Master Angler
Lol Brb
"Today we make our stand. Today we take back the Ruby Throne, which is ours by ancient right and the blessings of the Divines. Stand with us." — Queen Ayrenn