Should clothing be more expensive?

[Meezermouzer]

On a more serious note, medieval clothing was highly linked to status - and, unless I'm much mistaken, devs have claimed that the barbershop's clothing will be restricted accordingly.

Correct via CKIII FAQ

▲ Are clothes of characters strictly tied to their title like count and duke, and can we change their clothes and stuff?
► Yes the rank of a character decides how fancy clothes and headgear they have access to and yes you can change the clothing and hairstyles/beards in the barbershop

Another idea would be introducing rarity/customization for regalia. It could potentially be unlocked based on Renown or Splendor. Some way to make your character realistically "special" is a good thing I would say.

 

[Johann7]

And I'm not sure how clothing could have specific properties, except in very rare, supernatural cases (like the hide of the Nemean lion, the Megingjord or seven league boots).

I mean, the entire point of fancy clothing in Real Life is status signaling/prestige; protection from the elements can be achieved without dyes, frills, embroidery, etc. Opinion modifiers (including maluses for characters who abhor decadence or vanity) and prestige effects would make perfect sense.