It took 30 seconds to find this in IRS Pub 926:

Don't count as wages any of the following items.
• Meals provided to your employee at your home for
your convenience.
• Lodging provided to your employee at your home for
your convenience and as a condition of employment.

It's not that employer-furnished lodging is unusual in your part of the country.  It's that clients with nannies are not usual in your practice.  Believe it or not, there are probably 100,000 American families with live-in nannies who have asked and found answers to this question.  By the way, if they spend another $50,000 to remodel the kitchen, that's not deductible either even if they hire a cook.  Nor $25,000 for the walk-in closets suggested by the butler and valet.