There's also more of a lady and servant relationship in a one-to-one scenario. That's extremely uncomfortable for me. In a hotel, it's a job and some chains actually pay their employees quite well, making it a true profession. A professional job where no one is under you per se or serving you explicitly is much better than having people follow your every whim directly. There are buffer layers here and the hotel can very much say no and protect their employees if the guest goes too far.
Assuming $1.5k as a conservative estimate, we get about $550k/yr. Or, $45k/mo. If you have a mortgage, then for a marginally expensive home ($3M in the bay), a 20-year mortgage all in at 3% is $21k.
A good butler starts at around 9k/mo before taxes etc. And goes up to $12k/mo to $15k/mo. Let's assume $10k, then that's $31k so far.
Add about $6k more for household cleaning and a part-time chef (pricey!), then we get to $37k before the groceries are brought in.
Depending on how you shop, this can be between $2k/mo/head to $5k/mo/head. let's assume $2.5k. So $39.5k before utilities, upkeep etc are taken into account.
Add $2.5k in high-speed internet and utilities. If you want a house with a good HVAC system, air purification and all the other bells and whistles that are incidental in a hotel. We're now at $42k with a $3k difference so far. I'm sure that can be easily made up if you buy a more expensive property or the property taxes go up or you refurnish your home...
It's fairly price competitive to live in a hotel for a rich person versus having your own gigantic household. The biggest tradeoff is space. And I'm happy to do that for the greater peace of mind.
Not only you are comparing a “small suite” with a probably much larger $3mn home but you’re comparing renting with buying over 20 years. You should count only the interests paid.
In the past private school fags, or military batmen presumably might follow a "gentleman" in to later service, but I don't see where it fits in now? I'd guess it must be like being an equerry, about social positioning in the first place?