Socialist equality is evil because under it one person chooses not to work, the other works hard, and the one who chose not to is compensated by the hard worker. It both deminishes incentive to work and takes hard workers earnings. Children have no choice. Their wealth or place of residence is no fault of their own.
Although this is true enough, it is not the responsibility of the successful to make up for the inequalities of birth, nor the place of government to act as equalizer. That said, as a modern compromise to the "social responsibility to the least able" versus the anarchistic "blame your parents if your childhood sucks" question; I would not be opposed to the idea that every child (born to provable, net tax paying, citizens) be allocated a 'defined benefit' social net at birth, to be used as necessary until depleted. For example, the cost of childhood health care could be subsidized in this manner by granting each newborn a (as an example) $15K Health Savings Account when they are issued a social security number. (It's really difficult to fake out the SSA and get a new SSN) The SSA would be in charge of tracking the funds, and parents (or adult account holders) couldn't access those funds directly, but only as a tax fileing reimbursement with evidence that 1) the expenses were real 2) for the child in question and 3) the parents really didn't have the resources to pay for it. Even if the parents are denied recompensation, the fund remains the asset of the child, forever.
And I can solve the 'Universal health care' debate in two minutes. A state block-grant fund wherein any procedure or prescription drug that was medically available to the richest American 50 years prior to the current year could be paid for in it's entirety, regardless of who is asking for it. Excluding prescriptions that are now over the counter. And the procedure cannot have an updated version, either. So no heart surgery, no brain surgery, and very little cancer treatments for the destitute (pretty much exactly like it is now by default, with the 'obligation to treat' emergency room laws) but break a bone and you can go to any emergency room or urgent care center and have it set and cast without so much as the question "are you a US citizen".
These are certainly not libertarian viewpoints, but I think that they would be preferable to even the most hardcore libs to what we have now.
I know what is the best education for children.