I'll be blunt: This makes absolutely no sense. None.

You're buying for a room inside the current FC house you have. It's not a magical device that teleports for you and never was it even explained that this is what the room was. Therefore, you're literally paying for an extension within the FC. You are agreeing that paying 300k is basically that.

This isn't some addition to your character. It's an addiction to the FC. That's it. If you leave the FC, you lose that perk. It's not a character perk; considering the room is solely for vanity reasons, it's a gil sink.

Tying it to the character would require it to be reconsidered completely. This is why personal housing was introduced: you want your own place, get one of those. I will say that i completely understand price and spacing issues can cut into that but I vehemently disagree with having the personal room come with you no matter what FC you do. This is coming from someone who has a personal house AND a personal room in my FC.