Travel / multiple homes confuse the issue because nobody spends much time on their 5th house they use less than a month per year, so the decoration is mostly outsourced to 3rd parties.

The portion of rich people homes they actually use are often quite cluttered. The simple limitation of needing to walk to a room to use it means spreading out across a huge home gets annoying. Semi public spaces for guests on the other hand can look like hotels because that’s effectively what they are.

Space is a factor too. I toured the mansion one time a few years back because a friend of mine was remodeling it. The master bedroom was as large as my entire house. That's a single bedroom for the two people planned to live there. I saw it while it was still under construction and so completely unlivable and but you could quickly figure out which parts were intended for the people lived there to live in and which parts were semi-public most of the mansion was clearly public spaces where they would have parties.