I am from another country where paying for childcare cash in hand is fairly common and no one seems to question the moral implications of it.
I think as long as both parties are amenable to it then it isn't a problem. I know people who pay entire salaries under the table and others who won't even let their nanny babysit without declaring it and plenty inbetween.
However if a childcare provider (nanny, for example) wishes to receive a fully tax(ed/able) salary then either really the family should agree to it, or the childcare provider should not accept the job.
If I were hiring a nanny and I wished to pay partly in cash, I'd try and gauge the appetite of the nanny for being paid in that way before wasting his/her time.