The lunchbox thing is a red herring - IMO most children are capable of understanding that lunchboxes vary, even if they covet someone else's crisps rather than the gravel and honey they've been given.
When it comes to lifestyle stuff 'your child your rules' is fine, but when it comes to teaching the basics of how to exist in wider society as well as within your own family's culture then it has shortcomings as a policy.
'Your child your rules' becomes a real problem when it's practiced in the extreme, and those rules translate into fundamental conflicts between what parents teach their children in terms of basic manners, ethics and social norms.
One parent ignores their little darling stealing, attacking other children or damaging others' property; another parent reprimands their child for that kind of behaviour. When those two children grow up you have two adults, raised very differently, one of which takes social norms seriously and generally abides by them, and the other of which is at best ignorant of commonly accepted behaviour or at worst simply doesn't care, or doesn't believe they should be subject to such expectations.
Quite aside from the corrosive effects of thoughtless, selfish or uninhibited behaviour on other people, the person raised without reference to any social expectations is more likely to suffer from social exclusion; they will face an uphill struggle if they want to contribute to civic society as, unlike the child who was taught manners, they have to work out from first principles how to behave in an acceptable way.