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?