Of course, simply providing these services doesn't always cut it. Look at the generational poverty in the US "ghettoes" for obvious confirmation of this. But in general it's a good thing to do and it benefits people. It's certainly not impossible and definitely does not always miserably fail.
For maximum potential, I mostly mean the ability to do what you want in terms of jobs with only intelligence and work holding you back, not the circumstances you were born in.
What's your take on the current student loans situation where almost everyone is able to obtain resources to go to a limited number of colleges and pay for whichever degree they like? Should we expand this and instead of loaning money give it away for free, if this goes towards achieving maximum potential? In your opinion, how much would a regular 4 year degree cost in such a case?
Another model might be to increase subsidy for fields with more guaranteed profit centers, while decreasing the amount of subsidy for fields in which a career profit is less likely, such that loans are more likely to be paid off. This again may make college cheaper, and/or more accessible, but may fail to yield enough trained workers to deliver in necessary but unprofitable fields.
That said, I'm not just trying to poop on the idea, but to highlight that "cost" is not the only rubric of accessibility, and that "cheaper" doesn't necessarily yield the results you're looking for, and may actually result in contrary outcomes from what we expect.
Provided that I am willing to concede this point for the sake of the argument: what makes you think that your redistribution model will actually allow everyone to achieve their maximum potential?[1] Given that similar redistribution systems have been tried before, where governing bodies were thinking they actually know what's good for "everyone/society", but all of them miserably failed, what differentiates your proposed approach from what have been already implemented?
[1] I don't even know what "achieving maximum potential" means. Is it achieving someone's goals in life? Producing the most widgets possible? Killing as many unbelievers as possible to get into heaven?