I believe this is to not draw attention to the property. There was a Planet Money podcast a while ago about how high-end real estate is being used by foreigners to launder money. If the FBI catches wind, they have tools to seize the property and remunerate the proceeds.

I'm guessing that renting the property means involving the IRS and potentially their foreign counterparts in the person's home country, both of which could increase the likelihood of getting caught.

Because these houses are also safe retreats in case of upheaval in their home countries, and renters are occasionally hard to evict.

A colleague has a cousin that owns at least a couple of properties like this.

The penthouse apartment was available at all times to impress visitors (e.g. my colleague), and included a chauffeur who acted as a tour guide. The owner used it himself occasionally, if he was visiting the city for a business trip.

It's because there's a clear mathematical relationship between the price someone is willing to rent, the prevailing interest rate and the price a property is worth.

As an owner, you don't want that information to get out.

Squatters seem like they would cause a problem. These places probably have staffs for the upkeep though.

They don't rent them out.

Source: am Vancouverite