Civ III leaders changing clothes was a very fun element. As was the throne room in Civ II. As was palace customization in Civ I, along with the newspaper headlines. Why all such fun stuff keeps disappearing and getting replaced with... nothing of the sort? (well, at least wonder movies are back, very much appreciated, thank you for that!).
Firaxis could bring them all back, add customization to the leader clothing and... tie everything up into combined conditions for the revamped cultural victory - who cares about those tourists anyway? Only the coolest chief of state with the most fashionable attire, most stylish throne room and architecturally most graceful palace is worthy of the culture victory! The rivals will just shrivel and drop dead with envy and jealousy.
We could use new types of great people: great fashion designers, great interior designers and great architects. Earned with respective buildings or bought (patronage) they would unlock fashionable pieces of clothing, room decoration or architectural elements available to use for the customization of the leader's clothing, the throne room and the palace.
Something's missing...
Ah, yes, another type of GP - the great critic. After borrowing one or two elements from the existing religious mechanics, those pundits could establish certain schools or houses of fashion and their followers could travel around the world spreading the true word of fashion and ridiculing the dressing or decorating or building habits of the others. Later they could just publish articles taking benefit of the printing press or make appearances on the radio and TV via broadcast towers to reach much wider audiences.
Persuade other leaders that they dress like a scarecrow unless they buy your blue jeans (or specifically THAT shade of chest wax), that a barn interior looks better than their throne room unless they redecorate it after your fashion, that a big bad wolf is on its way to blow away their palace for the offence of being such en eyesore so they'd better hurry to buy the services of your architects, and you'll be the top culture vulture.
Great works of art, music and literature could also be included in this or condensed under a single great person of arts mechanic.
The general idea being - it is important not only to create nice things but to put a good spin on them as well - a good story is one of the longest living and most reliable currencies in human history.
Which conveniently brings me back to Civ III: in case you feel unserious enough or just not too overmature, I can recommend
a good story of fashion, unrequited love and revenge in style, all spiced up with fifth grade humor, on the Civ III Stories and Tales forum. No reason, none at all, except to kill some time with a bit of fun and illustrated reading until Firaxis finally hatches something out of those Steam DB depots.