I think it's pretty standard to have at least a partial gross-up if you're paying on the books. Think of it like sales tax when shopping online. Do you buy that new computer from Amazon who add on NY sales tax or Newegg who charge the same price but don't collect the tax? For a nanny, it's tough to justify taking an on-the-books job with lower take home pay.
You can argue that a full gross-up isn't necessary since there are ancillary benefits to being on-the-books (Social Security, Medicare, unemployment, etc.). But there are also some hidden pitfalls. I heard about a family recently who wanted to move their nanny on the books and were willing to gross-up to accomplish it, but the nanny would have lost her low-cost health insurance (not sure if it was Medicaid or what) because she would be making too much money to qualify, and they couldn't afford to pay for private health insurance. So off-the-books they remained.