Small's outnumber Mediums by a large margin, and there are less than a handful of Larges. The more populated a server, the harder it is to get an L, especially with the timer not being on since October for auto demolish.
Is the spaghetti code this game runs on too garbled to withstand a Ward+subdivision of majority M's and about five L's? Perhaps a tiny bit of S's sprinkled in ideal locations like the beach houses in Mist. There's an NPC blocking off a location in Gridania that interested me because as far as I know, nothing- not even a cutscene exists beyond that area where nobles live that the guard stops you from getting into. Ul'dah nobles have to live somewhere too and surely there's a privateer sitting pretty in La Noscea.
Now, I expect the argument of "just move if you want it so bad." However, even on low population worlds, Larges are still easily taken up- and again. No auto-demolish in months so they're just going to sit there.
This could be a separate ward from the main housing areas to represent exclusivity. Maybe add on a threshold for being able to purchase. In Shirogane's case, it's having access to Shiro in the first place. I would think a certain point of MSQ progression as a reasonable recognition of the WoL's efforts given how much gil and gear we've amassed since ARR.