IME, this is usually....but not always....something of a moot point.

If vouchers are involved for the restaurant, there's usually a finite number of coupons distributed. Usually one or two per day, depending on whether travelling alone or with a single companion. If there's a third person, etc., he or she usually has to pay. In this instance, three people could go to breakfast (Mom, Dad, offspring), but only one would be charged. All of this would vary by property.

If there's only one voucher, but more than one person in the room, it would be usable by whomever shows up in the restaurant....whether or not he or she is the plat member.

Most of the time, however, the free breakfast involves the CL lounge....in which case all keys for the same room would be encoded to let anyone posessing one gain entry. I've never seen an instance where bringing the kids along to the CL has resulted in someone being denied....but I'd guess that could certainly happen in cases of clear and blatant abuse.